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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 6098 | . 2 ⊢ (∀𝑥(𝑥 = 𝑦 ↔ 𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦) | |
2 | biid 253 | . 2 ⊢ (𝑥 = 𝑦 ↔ 𝑥 = 𝑦) | |
3 | 1, 2 | mpg 1898 | 1 ⊢ (℩𝑥𝑥 = 𝑦) = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 198 = wceq 1658 ℩cio 6085 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-9 2175 ax-10 2194 ax-11 2209 ax-12 2222 ax-13 2391 ax-ext 2804 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 881 df-tru 1662 df-ex 1881 df-nf 1885 df-sb 2070 df-clab 2813 df-cleq 2819 df-clel 2822 df-nfc 2959 df-rex 3124 df-v 3417 df-sbc 3664 df-un 3804 df-sn 4399 df-pr 4401 df-uni 4660 df-iota 6087 |
This theorem is referenced by: (None) |
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