Theorem iotabii 6496

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 6477	. 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 6462

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 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3449  df-ss 3931  df-uni 4872  df-iota 6464

This theorem is referenced by:  riotav  7349  riotarab  7386  ovtpos  8220  cbvsum  15661  cbvsumv  15662  cbvprod  15879  cbvprodv  15880  prodeq1i  15882  oppgid  19288  oppr1  20259  riotaeqbii  36186  sumeq2si  36190  prodeq2si  36192  cbvprodvw2  36235  fourierdlem89  46193  fourierdlem90  46194  fourierdlem91  46195  fourierdlem96  46200  fourierdlem97  46201  fourierdlem98  46202  fourierdlem99  46203  fourierdlem100  46204  fourierdlem112  46216