Theorem bnj1340

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

	Ref	Expression
Hypotheses	bnj1340.1	|- ( ps -> E. x th )
	bnj1340.2	|- ( ch <-> ( ps /\ th ) )
	bnj1340.3	|- ( ps -> A. x ps )
Assertion	bnj1340	|- ( ps -> E. x ch )

Proof

Step	Hyp	Ref	Expression
1		bnj1340.1	|- ( ps -> E. x th )
2		bnj1340.2	|- ( ch <-> ( ps /\ th ) )
3		bnj1340.3	|- ( ps -> A. x ps )
4	3 1	bnj596	|- ( ps -> E. x ( ps /\ th ) )
5	4 2	bnj1198	|- ( ps -> E. x ch )