Theorem bnj524

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj524.1	⊢ ( 𝜑 ↔ 𝜓 )
	bnj524.2	⊢ 𝐴 ∈ V
Assertion	bnj524	⊢ ( [ 𝐴 / 𝑥 ] 𝜑 ↔ [ 𝐴 / 𝑥 ] 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bnj524.1	⊢ ( 𝜑 ↔ 𝜓 )
2		bnj524.2	⊢ 𝐴 ∈ V
3	1	sbcbii	⊢ ( [ 𝐴 / 𝑥 ] 𝜑 ↔ [ 𝐴 / 𝑥 ] 𝜓 )