Theorem reximia 2572

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 2571	. 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 2534	1 |- ( E. x e. A ph -> E. x e. A ps )

Syntax hints:   -> wi 4   e. wcel 2148   E.wrex 2456

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534

This theorem depends on definitions:  df-bi 117  df-ral 2460  df-rex 2461

This theorem is referenced by:  reximi  2574  iunpw  4481  nsmallnqq  7411  1idprl  7589  1idpru  7590  qmulz  9623  zq  9626  caubnd2  11126  sin0pilem1  14205