Theorem iotabii 6466

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 6450	. 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 6435

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 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-ss 3919  df-uni 4860  df-iota 6437

This theorem is referenced by:  riotav  7308  riotarab  7345  ovtpos  8171  cbvsum  15599  cbvsumv  15600  cbvprod  15817  cbvprodv  15818  prodeq1i  15820  oppgid  19266  oppr1  20266  riotaeqbii  36231  sumeq2si  36235  prodeq2si  36237  cbvprodvw2  36280  fourierdlem89  46232  fourierdlem90  46233  fourierdlem91  46234  fourierdlem96  46239  fourierdlem97  46240  fourierdlem98  46241  fourierdlem99  46242  fourierdlem100  46243  fourierdlem112  46255