Theorem exsimpr 1646

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 461	. 2 |- ( ( ph /\ ps ) -> ps )
2	1	eximi 1626	1 |- ( E. x ( ph /\ ps ) -> E. x ps )

Syntax hints:   -> wi 4   /\ wa 369   E.wex 1587

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588

This theorem is referenced by:  19.40  1647  spsbe  1706  euanOLD  2341  rexex  2893  imassrn  5289  fv3  5813  finacn  8332  dfac4  8404  kmlem2  8432  ac6c5  8763  ac6s3  8768  ac6s5  8772  ac6s3f  29132  bj-finsumval0  32922