| Mathbox for Alexander van der Vekens |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > icheqid | Structured version Visualization version GIF version | ||
| Description: In an equality for the same setvar variable, the setvar variable is interchangeable by itself. Special case of ichid 47438 and icheq 47449 without distinct variables restriction. (Contributed by AV, 29-Jul-2023.) |
| Ref | Expression |
|---|---|
| icheqid | ⊢ [𝑥⇄𝑥]𝑥 = 𝑥 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ichid 47438 | 1 ⊢ [𝑥⇄𝑥]𝑥 = 𝑥 |
| Colors of variables: wff setvar class |
| Syntax hints: [wich 47432 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-12 2177 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-sb 2065 df-ich 47433 |
| This theorem is referenced by: (None) |
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