Theorem bnj596

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

	Ref	Expression
Hypotheses	bnj596.1	|- ( ph -> A. x ph )
	bnj596.2	|- ( ph -> E. x ps )
Assertion	bnj596	|- ( ph -> E. x ( ph /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		bnj596.1	|- ( ph -> A. x ph )
2		bnj596.2	|- ( ph -> E. x ps )
3	2	ancli	|- ( ph -> ( ph /\ E. x ps ) )
4	1	nf5i	|- F/ x ph
5	4	19.42	|- ( E. x ( ph /\ ps ) <-> ( ph /\ E. x ps ) )
6	3 5	sylibr	|- ( ph -> E. x ( ph /\ ps ) )