Theorem vtoclALT

Description: Alternate proof of vtocl . Shorter but requires more axioms. (Contributed by NM, 30-Aug-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	vtocl.1	⊢ 𝐴 ∈ V
	vtocl.2	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
	vtocl.3	⊢ 𝜑
Assertion	vtoclALT	⊢ 𝜓

Proof

Step	Hyp	Ref	Expression
1		vtocl.1	⊢ 𝐴 ∈ V
2		vtocl.2	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
3		vtocl.3	⊢ 𝜑
4		nfv	⊢ Ⅎ 𝑥 𝜓
5	4 1 2 3	vtoclf	⊢ 𝜓