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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 6099 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓)) | |
2 | iotabii.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
3 | 1, 2 | mpg 1896 | 1 ⊢ (℩𝑥𝜑) = (℩𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 198 = wceq 1656 ℩cio 6088 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-9 2173 ax-10 2192 ax-11 2207 ax-12 2220 ax-ext 2803 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 879 df-tru 1660 df-ex 1879 df-nf 1883 df-sb 2068 df-clab 2812 df-cleq 2818 df-clel 2821 df-nfc 2958 df-rex 3123 df-uni 4661 df-iota 6090 |
This theorem is referenced by: riotav 6876 ovtpos 7637 cbvsum 14809 cbvprod 15025 oppgid 18143 oppr1 18995 fourierdlem89 41200 fourierdlem90 41201 fourierdlem91 41202 fourierdlem96 41207 fourierdlem97 41208 fourierdlem98 41209 fourierdlem99 41210 fourierdlem100 41211 fourierdlem112 41223 |
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