Theorem iotabii 6477

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 6461	. 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
2		iotabii.1	. 2 ⊢ (𝜑 ↔ 𝜓)
3	1, 2	mpg 1798	1 ⊢ (℩𝑥𝜑) = (℩𝑥𝜓)

Syntax hints:   ↔ wb 206   = wceq 1541  ℩cio 6446

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3442  df-ss 3918  df-uni 4864  df-iota 6448

This theorem is referenced by:  riotav  7320  riotarab  7357  ovtpos  8183  cbvsum  15618  cbvsumv  15619  cbvprod  15836  cbvprodv  15837  prodeq1i  15839  oppgid  19285  oppr1  20286  riotaeqbii  36392  sumeq2si  36396  prodeq2si  36398  cbvprodvw2  36441  dfpre  38646  fourierdlem89  46435  fourierdlem90  46436  fourierdlem91  46437  fourierdlem96  46442  fourierdlem97  46443  fourierdlem98  46444  fourierdlem99  46445  fourierdlem100  46446  fourierdlem112  46458