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Mirrors > Home > MPE Home > Th. List > iotabii | Structured version Visualization version GIF version |
Description: Formula-building deduction for iota. (Contributed by Mario Carneiro, 2-Oct-2015.) |
Ref | Expression |
---|---|
iotabii.1 | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
iotabii | ⊢ (℩𝑥𝜑) = (℩𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iotabi 6509 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓)) | |
2 | iotabii.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
3 | 1, 2 | mpg 1798 | 1 ⊢ (℩𝑥𝜑) = (℩𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 = wceq 1540 ℩cio 6493 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1543 df-ex 1781 df-sb 2067 df-clab 2709 df-cleq 2723 df-clel 2809 df-v 3475 df-in 3955 df-ss 3965 df-uni 4909 df-iota 6495 |
This theorem is referenced by: riotav 7373 riotarab 7411 ovtpos 8232 cbvsum 15648 cbvprod 15866 oppgid 19271 oppr1 20248 fourierdlem89 45372 fourierdlem90 45373 fourierdlem91 45374 fourierdlem96 45379 fourierdlem97 45380 fourierdlem98 45381 fourierdlem99 45382 fourierdlem100 45383 fourierdlem112 45395 |
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