Theorem vtoclgOLD 3565

Description: Obsolete version of vtoclg 3564 as of 20-Apr-2024. (Contributed by NM, 17-Apr-1995.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
vtoclgOLD.1	⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓))
vtoclgOLD.2	⊢ 𝜑

Assertion

Ref	Expression
vtoclgOLD	⊢ (𝐴 ∈ 𝑉 → 𝜓)

Distinct variable groups:   𝑥,𝐴   𝜓,𝑥

Allowed substitution hints:   𝜑(𝑥)   𝑉(𝑥)

Proof of Theorem vtoclgOLD

Step	Hyp	Ref	Expression
1		nfv 1914	. 2 ⊢ Ⅎ𝑥𝜓
2		vtoclgOLD.1	. 2 ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓))
3		vtoclgOLD.2	. 2 ⊢ 𝜑
4	1, 2, 3	vtoclg1f 3563	1 ⊢ (𝐴 ∈ 𝑉 → 𝜓)

Syntax hints:   → wi 4   ↔ wb 208   = wceq 1536   ∈ wcel 2113

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-12 2176  ax-ext 2792

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1780  df-nf 1784  df-cleq 2813  df-clel 2892

This theorem is referenced by: (None)