Theorem reximia 2720

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 10-Feb-1997.)

Hypothesis

Ref	Expression
reximia.1	|- (x e. A -> (ph -> ps))

Assertion

Ref	Expression
reximia	|- (E.x e. A ph -> E.x e. A ps)

Proof of Theorem reximia

Step	Hyp	Ref	Expression
1		rexim 2719	. 2 |- (A.x e. A (ph -> ps) -> (E.x e. A ph -> E.x e. A ps))
2		reximia.1	. 2 |- (x e. A -> (ph -> ps))
3	1, 2	mprg 2684	1 |- (E.x e. A ph -> E.x e. A ps)

This proof depends on syntax axioms:   -> wi 4   e. wcel 1710  E.wrex 2616

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This proof depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-ral 2620  df-rex 2621

This theorem is used by:  reximi  2722