Theorem bnj1345

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

	Ref	Expression
Hypotheses	bnj1345.1	|- ( ph -> E. x ( ps /\ ch ) )
	bnj1345.2	|- ( th <-> ( ph /\ ps /\ ch ) )
	bnj1345.3	|- ( ph -> A. x ph )
Assertion	bnj1345	|- ( ph -> E. x th )

Proof

Step	Hyp	Ref	Expression
1		bnj1345.1	|- ( ph -> E. x ( ps /\ ch ) )
2		bnj1345.2	|- ( th <-> ( ph /\ ps /\ ch ) )
3		bnj1345.3	|- ( ph -> A. x ph )
4	1 3	bnj1275	|- ( ph -> E. x ( ph /\ ps /\ ch ) )
5	4 2	bnj1198	|- ( ph -> E. x th )