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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 6529 | . 2 ⊢ (∀𝑥(𝑥 = 𝑦 ↔ 𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦) | |
2 | biid 261 | . 2 ⊢ (𝑥 = 𝑦 ↔ 𝑥 = 𝑦) | |
3 | 1, 2 | mpg 1792 | 1 ⊢ (℩𝑥𝑥 = 𝑦) = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 206 = wceq 1535 ℩cio 6508 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1963 ax-7 2003 ax-8 2106 ax-9 2114 ax-ext 2704 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-tru 1538 df-ex 1775 df-sb 2061 df-clab 2711 df-cleq 2725 df-clel 2812 df-v 3479 df-un 3968 df-ss 3980 df-sn 4631 df-pr 4633 df-uni 4915 df-iota 6510 |
This theorem is referenced by: (None) |
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