Theorem bnj228

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 9-Jul-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj228.1	|- ( ph <-> A. x e. A ps )
Assertion	bnj228	|- ( ( x e. A /\ ph ) -> ps )

Proof

Step	Hyp	Ref	Expression
1		bnj228.1	|- ( ph <-> A. x e. A ps )
2		rsp	|- ( A. x e. A ps -> ( x e. A -> ps ) )
3	1 2	sylbi	|- ( ph -> ( x e. A -> ps ) )
4	3	impcom	|- ( ( x e. A /\ ph ) -> ps )