Theorem cbviotavwOLD 6534

Description: Obsolete version of cbviotavw 6533 as of 30-Sep-2024. (Contributed by Andrew Salmon, 1-Aug-2011.) (Revised by GG, 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 1913	. 2 ⊢ Ⅎ𝑦𝜑
3		nfv 1913	. 2 ⊢ Ⅎ𝑥𝜓
4	1, 2, 3	cbviotaw 6532	1 ⊢ (℩𝑥𝜑) = (℩𝑦𝜓)

Syntax hints:   → wi 4   ↔ wb 206   = wceq 1537  ℩cio 6523

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2158  ax-12 2178  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-ex 1778  df-nf 1782  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-ss 3993  df-sn 4649  df-uni 4932  df-iota 6525

This theorem is referenced by: (None)