Theorem sbcg

Description: Substitution for a variable not occurring in a wff does not affect it. Distinct variable form of sbcgf . (Contributed by Alan Sare, 10-Nov-2012)

	Ref	Expression
Assertion	sbcg	⊢ ( 𝐴 ∈ 𝑉 → ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		nfv	⊢ Ⅎ 𝑥 𝜑
2	1	sbcgf	⊢ ( 𝐴 ∈ 𝑉 → ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜑 ) )