Theorem bnj538

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.) (Proof shortened by OpenAI, 30-Mar-2020)

	Ref	Expression
Hypothesis	bnj538.1	|- A e. _V
Assertion	bnj538	|- ( [. A / y ]. A. x e. B ph <-> A. x e. B [. A / y ]. ph )

Proof

Step	Hyp	Ref	Expression
1		bnj538.1	|- A e. _V
2		sbcralg	|- ( A e. _V -> ( [. A / y ]. A. x e. B ph <-> A. x e. B [. A / y ]. ph ) )
3	1 2	ax-mp	|- ( [. A / y ]. A. x e. B ph <-> A. x e. B [. A / y ]. ph )