Theorem bnj1275

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

	Ref	Expression
Hypotheses	bnj1275.1	|- ( ph -> E. x ( ps /\ ch ) )
	bnj1275.2	|- ( ph -> A. x ph )
Assertion	bnj1275	|- ( ph -> E. x ( ph /\ ps /\ ch ) )

Proof

Step	Hyp	Ref	Expression
1		bnj1275.1	|- ( ph -> E. x ( ps /\ ch ) )
2		bnj1275.2	|- ( ph -> A. x ph )
3	2 1	bnj596	|- ( ph -> E. x ( ph /\ ( ps /\ ch ) ) )
4		3anass	|- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
5	3 4	bnj1198	|- ( ph -> E. x ( ph /\ ps /\ ch ) )