Theorem bnj1196

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

	Ref	Expression
Hypothesis	bnj1196.1	|- ( ph -> E. x e. A ps )
Assertion	bnj1196	|- ( ph -> E. x ( x e. A /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		bnj1196.1	|- ( ph -> E. x e. A ps )
2		df-rex	|- ( E. x e. A ps <-> E. x ( x e. A /\ ps ) )
3	1 2	sylib	|- ( ph -> E. x ( x e. A /\ ps ) )