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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 6471 | . 2 ⊢ (∀𝑥(𝑥 = 𝑦 ↔ 𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦) | |
2 | biid 261 | . 2 ⊢ (𝑥 = 𝑦 ↔ 𝑥 = 𝑦) | |
3 | 1, 2 | mpg 1800 | 1 ⊢ (℩𝑥𝑥 = 𝑦) = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 = wceq 1542 ℩cio 6450 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3449 df-un 3919 df-in 3921 df-ss 3931 df-sn 4591 df-pr 4593 df-uni 4870 df-iota 6452 |
This theorem is referenced by: (None) |
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