Mathbox for Andrew Salmon |
< Previous
Next >
Nearby theorems |
||
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 6322 | . 2 ⊢ (∀𝑥(𝑥 = 𝑦 ↔ 𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦) | |
2 | biid 263 | . 2 ⊢ (𝑥 = 𝑦 ↔ 𝑥 = 𝑦) | |
3 | 1, 2 | mpg 1792 | 1 ⊢ (℩𝑥𝑥 = 𝑦) = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 = wceq 1531 ℩cio 6305 |
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 1905 ax-6 1964 ax-7 2009 ax-8 2110 ax-9 2118 ax-10 2139 ax-11 2154 ax-12 2170 ax-ext 2791 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1534 df-ex 1775 df-nf 1779 df-sb 2064 df-clab 2798 df-cleq 2812 df-clel 2891 df-nfc 2961 df-rex 3142 df-v 3495 df-sbc 3771 df-un 3939 df-sn 4560 df-pr 4562 df-uni 4831 df-iota 6307 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |