Theorem bnj1459

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

	Ref	Expression
Hypotheses	bnj1459.1	|- ( ps <-> ( ph /\ x e. A ) )
	bnj1459.2	|- ( ps -> ch )
Assertion	bnj1459	|- ( ph -> A. x e. A ch )

Proof

Step	Hyp	Ref	Expression
1		bnj1459.1	|- ( ps <-> ( ph /\ x e. A ) )
2		bnj1459.2	|- ( ps -> ch )
3	1 2	sylbir	|- ( ( ph /\ x e. A ) -> ch )
4	3	ralrimiva	|- ( ph -> A. x e. A ch )