Theorem cbviotav 6526

Description: Change bound variables in a description binder. Usage of this theorem is discouraged because it depends on ax-13 2375. Use the weaker cbviotavw 6524 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 1912	. 2 ⊢ Ⅎ𝑦𝜑
3		nfv 1912	. 2 ⊢ Ⅎ𝑥𝜓
4	1, 2, 3	cbviota 6525	1 ⊢ (℩𝑥𝜑) = (℩𝑦𝜓)

Syntax hints:   → wi 4   ↔ wb 206   = wceq 1537  ℩cio 6514

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-13 2375  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-ss 3980  df-sn 4632  df-uni 4913  df-iota 6516

This theorem is referenced by: (None)