Theorem iotabii 6483

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 6467	. 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
2		iotabii.1	. 2 ⊢ (𝜑 ↔ 𝜓)
3	1, 2	mpg 1799	1 ⊢ (℩𝑥𝜑) = (℩𝑥𝜓)

Syntax hints:   ↔ wb 206   = wceq 1542  ℩cio 6452

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3431  df-ss 3906  df-uni 4851  df-iota 6454

This theorem is referenced by:  riotav  7329  riotarab  7366  ovtpos  8191  cbvsum  15657  cbvsumv  15658  cbvprod  15878  cbvprodv  15879  prodeq1i  15881  oppgid  19331  oppr1  20330  riotaeqbii  36380  sumeq2si  36384  prodeq2si  36386  cbvprodvw2  36429  dfpre  38797  fourierdlem89  46623  fourierdlem90  46624  fourierdlem91  46625  fourierdlem96  46630  fourierdlem97  46631  fourierdlem98  46632  fourierdlem99  46633  fourierdlem100  46634  fourierdlem112  46646