Theorem bnj1276

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

	Ref	Expression
Hypotheses	bnj1276.1	|- ( ph -> A. x ph )
	bnj1276.2	|- ( ps -> A. x ps )
	bnj1276.3	|- ( ch -> A. x ch )
	bnj1276.4	|- ( th <-> ( ph /\ ps /\ ch ) )
Assertion	bnj1276	|- ( th -> A. x th )

Proof

Step	Hyp	Ref	Expression
1		bnj1276.1	|- ( ph -> A. x ph )
2		bnj1276.2	|- ( ps -> A. x ps )
3		bnj1276.3	|- ( ch -> A. x ch )
4		bnj1276.4	|- ( th <-> ( ph /\ ps /\ ch ) )
5	1 2 3	hb3an	|- ( ( ph /\ ps /\ ch ) -> A. x ( ph /\ ps /\ ch ) )
6	4 5	hbxfrbi	|- ( th -> A. x th )