Theorem vtoclgOLD

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

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

Proof

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