Theorem spcv

Description: Rule of specialization, using implicit substitution. (Contributed by NM, 22-Jun-1994)

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

Proof

Step	Hyp	Ref	Expression
1		spcv.1	⊢ 𝐴 ∈ V
2		spcv.2	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
3	2	spcgv	⊢ ( 𝐴 ∈ V → ( ∀ 𝑥 𝜑 → 𝜓 ) )
4	1 3	ax-mp	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )