Theorem sbcieg

Description: Conversion of implicit substitution to explicit class substitution. (Contributed by NM, 10-Nov-2005)

	Ref	Expression
Hypothesis	sbcieg.1	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
Assertion	sbcieg	⊢ ( 𝐴 ∈ 𝑉 → ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		sbcieg.1	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
2		nfv	⊢ Ⅎ 𝑥 𝜓
3	2 1	sbciegf	⊢ ( 𝐴 ∈ 𝑉 → ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜓 ) )