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| Mirrors > Home > MPE Home > Th. List > Mathboxes > iotaequ | Structured version Visualization version GIF version | ||
| Description: Theorem *14.2 in [WhiteheadRussell] p. 189. (Contributed by Andrew Salmon, 11-Jul-2011.) |
| Ref | Expression |
|---|---|
| iotaequ | ⊢ (℩𝑥𝑥 = 𝑦) = 𝑦 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | iotaval 6530 | . 2 ⊢ (∀𝑥(𝑥 = 𝑦 ↔ 𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦) | |
| 2 | biid 261 | . 2 ⊢ (𝑥 = 𝑦 ↔ 𝑥 = 𝑦) | |
| 3 | 1, 2 | mpg 1797 | 1 ⊢ (℩𝑥𝑥 = 𝑦) = 𝑦 |
| Colors of variables: wff setvar class |
| Syntax hints: ↔ wb 206 = wceq 1540 ℩cio 6510 |
| 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-8 2110 ax-9 2118 ax-ext 2707 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2714 df-cleq 2728 df-clel 2815 df-v 3481 df-un 3955 df-ss 3967 df-sn 4625 df-pr 4627 df-uni 4906 df-iota 6512 |
| This theorem is referenced by: (None) |
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