Theorem iotabii 6333

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 6320	. 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
2		iotabii.1	. 2 ⊢ (𝜑 ↔ 𝜓)
3	1, 2	mpg 1792	1 ⊢ (℩𝑥𝜑) = (℩𝑥𝜓)

Syntax hints:   ↔ wb 208   = wceq 1531  ℩cio 6305

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-8 2110  ax-9 2118  ax-ext 2791

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1775  df-sb 2064  df-clab 2798  df-cleq 2812  df-clel 2891  df-rex 3142  df-uni 4831  df-iota 6307

This theorem is referenced by:  riotav  7111  ovtpos  7899  cbvsum  15044  cbvprod  15261  oppgid  18476  oppr1  19376  fourierdlem89  42470  fourierdlem90  42471  fourierdlem91  42472  fourierdlem96  42477  fourierdlem97  42478  fourierdlem98  42479  fourierdlem99  42480  fourierdlem100  42481  fourierdlem112  42493