# base/not-exists-to-nexists

Rewrite \not\exists to the canonical AMS \nexists character when the target is available.

https://texform.dev/rules/base/not-exists-to-nexists

## Metadata

| Field | Value |
| --- | --- |
| Key | base/not-exists-to-nexists |
| Level | authoring |
| Fidelity | render |
| Enabled by packages | base |
| Profiles | Authoring, Faithful, Corpus, Equiv |

## Rewrite patterns

### command

From:

```latex
\not\exists
```

To:

```latex
\nexists
```

### literal

From:

```latex
\not∃
```

To:

```latex
\nexists
```

## Examples

Examples show the rule in isolation, not a complete normalization profile.

### Command

Before:

```latex
\not\exists x
```

After this rule:

```latex
\nexists x
```

Packages: base, ams.

Rendering verified with the declared packages.

### Literal

Before:

```latex
\not∃ x
```

After this rule:

```latex
\nexists x
```

Packages: base, ams.

Rendering verified with the declared packages.

## Triggers

- [\\not](https://texform.dev/latex/commands/not)

## Produces

- [\\nexists](https://texform.dev/latex/symbols/nexists)

## Touches

- [\\not](https://texform.dev/latex/commands/not)
- [\\exists](https://texform.dev/latex/symbols/exists)

## Same family

- [ams/Doteq-to-doteqdot](https://texform.dev/rules/ams/Doteq-to-doteqdot): Collapse Doteq to the descriptive doteqdot character.
- [ams/doublecap-to-Cap](https://texform.dev/rules/ams/doublecap-to-Cap): Collapse doublecap to the more common Cap character.
- [ams/gggtr-to-ggg](https://texform.dev/rules/ams/gggtr-to-ggg): Collapse gggtr to the shorter ggg character.
- [ams/llless-to-lll](https://texform.dev/rules/ams/llless-to-lll): Collapse llless to the shorter lll character.
- [ams/trianglerighteq-to-unrhd](https://texform.dev/rules/ams/trianglerighteq-to-unrhd): Collapse trianglerighteq to the more common unrhd character.
- [ams/unlhd-to-trianglelefteq](https://texform.dev/rules/ams/unlhd-to-trianglelefteq): Collapse unlhd to the descriptive trianglelefteq character.
- [ams/vartriangleleft-to-lhd](https://texform.dev/rules/ams/vartriangleleft-to-lhd): Collapse vartriangleleft to the more common lhd character.
- [ams/vartriangleright-to-rhd](https://texform.dev/rules/ams/vartriangleright-to-rhd): Collapse vartriangleright to the more common rhd character.
- [ams/impliedby-to-Longleftarrow](https://texform.dev/rules/ams/impliedby-to-Longleftarrow): Collapse impliedby to the explicit AMS long-left-arrow spelling with source-backed spacing.
- [ams/implies-to-Longrightarrow](https://texform.dev/rules/ams/implies-to-Longrightarrow): Collapse implies to the explicit AMS long-right-arrow spelling with source-backed spacing.
- [ams/Join-to-bowtie](https://texform.dev/rules/ams/Join-to-bowtie): Normalize Join to bowtie for corpus form.
- [ams/centerdot-to-cdot](https://texform.dev/rules/ams/centerdot-to-cdot): Normalize AMS centerdot to the base cdot character for corpus form.
- [ams/doublecup-to-Cup](https://texform.dev/rules/ams/doublecup-to-Cup): Normalize doublecup to Cup for corpus form.
- [ams/leadsto-to-rightsquigarrow](https://texform.dev/rules/ams/leadsto-to-rightsquigarrow): Normalize leadsto to the more common rightsquigarrow corpus form.
- [ams/lozenge-to-Diamond](https://texform.dev/rules/ams/lozenge-to-Diamond): Normalize lozenge to Diamond for corpus form.
- [ams/restriction-to-upharpoonright](https://texform.dev/rules/ams/restriction-to-upharpoonright): Normalize restriction to upharpoonright for corpus form.
- [ams/square-to-Box](https://texform.dev/rules/ams/square-to-Box): Normalize square to Box for corpus form.
- [ams/vartriangle-to-bigtriangleup](https://texform.dev/rules/ams/vartriangle-to-bigtriangleup): Normalize vartriangle to bigtriangleup for corpus form.
- [base/ast-to-asterisk](https://texform.dev/rules/base/ast-to-asterisk): Canonicalize the math binary operator \ast to the pixel-identical literal asterisk form.
- [base/ge-to-geq](https://texform.dev/rules/base/ge-to-geq): Collapse ge to the explicit geq relation character.
- [base/le-to-leq](https://texform.dev/rules/base/le-to-leq): Collapse le to the explicit leq relation character.
- [base/lnot-to-neg](https://texform.dev/rules/base/lnot-to-neg): Collapse lnot to the standard neg character.
- [base/ne-to-neq](https://texform.dev/rules/base/ne-to-neq): Collapse ne to the explicit neq relation character.
- [base/owns-to-ni](https://texform.dev/rules/base/owns-to-ni): Collapse owns to the shorter ni character.
- [base/prime-to-prime-node](https://texform.dev/rules/base/prime-to-prime-node): Convert the prime control sequence to the Prime AST node.
- [base/not-equals-to-neq](https://texform.dev/rules/base/not-equals-to-neq): Rewrite \not followed by an equals sign to the canonical \neq character.
- [base/not-in-to-notin](https://texform.dev/rules/base/not-in-to-notin): Rewrite \not\in to the canonical \notin character.
- [base/not-right-arrow-to-nrightarrow](https://texform.dev/rules/base/not-right-arrow-to-nrightarrow): Rewrite not followed by a U+2192 right arrow to the canonical AMS nrightarrow character.
- [base/dots-to-ldots-or-cdots](https://texform.dev/rules/base/dots-to-ldots-or-cdots): Resolve plain \dots to an explicit ellipsis only when the following math atom class determines MathJax's choice.
- [base/gets-to-leftarrow](https://texform.dev/rules/base/gets-to-leftarrow): Normalize gets to leftarrow for corpus form.
- [base/land-to-wedge](https://texform.dev/rules/base/land-to-wedge): Normalize land to wedge for corpus form.
- [base/lor-to-vee](https://texform.dev/rules/base/lor-to-vee): Normalize lor to vee for corpus form.
- [base/rightarrow-to-to](https://texform.dev/rules/base/rightarrow-to-to): Normalize rightarrow to the shorter to arrow character for corpus form.
- [base/semantic-dots-to-cdots](https://texform.dev/rules/base/semantic-dots-to-cdots): Normalize semantic centered-dot ellipsis aliases to cdots for corpus form.
- [base/semantic-dots-to-ldots](https://texform.dev/rules/base/semantic-dots-to-ldots): Normalize semantic baseline ellipsis aliases to ldots for corpus form.
- [physics/divsymbol-to-divisionsymbol](https://texform.dev/rules/physics/divsymbol-to-divisionsymbol): Collapse divsymbol to the documented divisionsymbol character alias.
- [physics/dotproduct-to-vdot](https://texform.dev/rules/physics/dotproduct-to-vdot): Collapse dotproduct to the shorter vdot character alias.
- [physics/cross-aliases-to-times](https://texform.dev/rules/physics/cross-aliases-to-times): Normalize physics cross-product glyph aliases to times for corpus form.

## Notes

Uses the exact MathJax not_remap entry U+2203 -> U+2204. Accept a bare U+2203 Char or the zero-argument known exists character command. The source owner remains base because not is a base command; AMS is required only for the produced character target, whose availability must guard the rule. Both atoms must occupy the same Root or Group child slot. Scripted, arguments, unknown nodes, Error, Environment, and cross-slot content fail closed. Consume not and its sibling atomically. Every Applied result removes the matched cmd:not node and its exists sibling; all other shapes return Skipped, so the number of eligible cmd:not nodes strictly decreases.

## Disable this rule

```python
TransformEngine(profile="corpus", disable_rules=["base/not-exists-to-nexists"])
```

```javascript
new TransformEngine({ profile: 'corpus', disableRules: ['base/not-exists-to-nexists'] })
```

[Open in Playground](https://play.texform.dev/?input=%5Cnot%5Cexists+x)