Theorem cbviotavwOLD 6504

Description: Obsolete version of cbviotavw 6503 as of 30-Sep-2024. (Contributed by Andrew Salmon, 1-Aug-2011.) (Revised by Gino Giotto, 26-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

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

Distinct variable groups:   𝜑,𝑦   𝜓,𝑥   𝑥,𝑦

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

Proof of Theorem cbviotavwOLD

Step	Hyp	Ref	Expression
1		cbviotavwOLD.1	. 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓))
2		nfv 1909	. 2 ⊢ Ⅎ𝑦𝜑
3		nfv 1909	. 2 ⊢ Ⅎ𝑥𝜓
4	1, 2, 3	cbviotaw 6502	1 ⊢ (℩𝑥𝜑) = (℩𝑦𝜓)

Syntax hints:   → wi 4   ↔ wb 205   = wceq 1533  ℩cio 6493

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2166  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3465  df-ss 3958  df-sn 4626  df-uni 4905  df-iota 6495

This theorem is referenced by: (None)