Theorem bnj525

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

	Ref	Expression
Hypothesis	bnj525.1	⊢ 𝐴 ∈ V
Assertion	bnj525	⊢ ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		bnj525.1	⊢ 𝐴 ∈ V
2		sbcg	⊢ ( 𝐴 ∈ V → ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜑 ) )
3	1 2	ax-mp	⊢ ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜑 )