Theorem exsimpr 1683

Description: Simplification of an existentially quantified conjunction. (Contributed by Rodolfo Medina, 25-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)

Assertion

Ref	Expression
exsimpr	|- ( E. x ( ph /\ ps ) -> E. x ps )

Proof of Theorem exsimpr

Step	Hyp	Ref	Expression
1		simpr 459	. 2 |- ( ( ph /\ ps ) -> ps )
2	1	eximi 1661	1 |- ( E. x ( ph /\ ps ) -> E. x ps )

Syntax hints:   -> wi 4   /\ wa 367   E.wex 1617

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636

This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618

This theorem is referenced by:  19.40  1684  spsbe  1748  rexex  2911  imassrn  5336  fv3  5861  finacn  8422  dfac4  8494  kmlem2  8522  ac6c5  8853  ac6s3  8858  ac6s5  8862  ceqsexv2d  27598  heiborlem3  30552  ac6s3f  30822  bj-finsumval0  35082