Theorem vtocle

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993)

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

Proof

Step	Hyp	Ref	Expression
1		vtocle.1	⊢ 𝐴 ∈ V
2		vtocle.2	⊢ ( 𝑥 = 𝐴 → 𝜑 )
3	2	vtocleg	⊢ ( 𝐴 ∈ V → 𝜑 )
4	1 3	ax-mp	⊢ 𝜑