Theorem exsimpr 1724

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 462	. 2 |- ( ( ph /\ ps ) -> ps )
2	1	eximi 1701	1 |- ( E. x ( ph /\ ps ) -> E. x ps )

Syntax hints:   -> wi 4   /\ wa 370   E.wex 1657

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676

This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658

This theorem is referenced by:  19.40  1725  spsbe  1794  rexex  2821  imassrn  5141  fv3  5838  finacn  8432  dfac4  8504  kmlem2  8532  ac6c5  8863  ac6s3  8868  ac6s5  8872  ceqsexv2d  28076  bj-finsumval0  31609  mptsnunlem  31647  topdifinffinlem  31657  heiborlem3  32052  ac6s3f  32321