Theorem cbviotav 6523

Description: Change bound variables in a description binder. Usage of this theorem is discouraged because it depends on ax-13 2376. Use the weaker cbviotavw 6521 when possible. (Contributed by Andrew Salmon, 1-Aug-2011.) (New usage is discouraged.)

Hypothesis

Ref	Expression
cbviotav.1	⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓))

Assertion

Ref	Expression
cbviotav	⊢ (℩𝑥𝜑) = (℩𝑦𝜓)

Distinct variable groups:   𝜑,𝑦   𝜓,𝑥

Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem cbviotav

Step	Hyp	Ref	Expression
1		cbviotav.1	. 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓))
2		nfv 1913	. 2 ⊢ Ⅎ𝑦𝜑
3		nfv 1913	. 2 ⊢ Ⅎ𝑥𝜓
4	1, 2, 3	cbviota 6522	1 ⊢ (℩𝑥𝜑) = (℩𝑦𝜓)

Syntax hints:   → wi 4   ↔ wb 206   = wceq 1539  ℩cio 6511

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-10 2140  ax-11 2156  ax-12 2176  ax-13 2376  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-nf 1783  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-ss 3967  df-sn 4626  df-uni 4907  df-iota 6513

This theorem is referenced by: (None)