Theorem iotabii 6499

Description: Formula-building deduction for iota. (Contributed by Mario Carneiro, 2-Oct-2015.)

Hypothesis

Ref	Expression
iotabii.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
iotabii	⊢ (℩𝑥𝜑) = (℩𝑥𝜓)

Proof of Theorem iotabii

Step	Hyp	Ref	Expression
1		iotabi 6480	. 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
2		iotabii.1	. 2 ⊢ (𝜑 ↔ 𝜓)
3	1, 2	mpg 1797	1 ⊢ (℩𝑥𝜑) = (℩𝑥𝜓)

Syntax hints:   ↔ wb 206   = wceq 1540  ℩cio 6465

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-ss 3934  df-uni 4875  df-iota 6467

This theorem is referenced by:  riotav  7352  riotarab  7389  ovtpos  8223  cbvsum  15668  cbvsumv  15669  cbvprod  15886  cbvprodv  15887  prodeq1i  15889  oppgid  19295  oppr1  20266  riotaeqbii  36193  sumeq2si  36197  prodeq2si  36199  cbvprodvw2  36242  fourierdlem89  46200  fourierdlem90  46201  fourierdlem91  46202  fourierdlem96  46207  fourierdlem97  46208  fourierdlem98  46209  fourierdlem99  46210  fourierdlem100  46211  fourierdlem112  46223