Theorem exsimpr 1738

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 468	. 2 |- ( ( ph /\ ps ) -> ps )
2	1	eximi 1715	1 |- ( E. x ( ph /\ ps ) -> E. x ps )

Syntax hints:   -> wi 4   /\ wa 376   E.wex 1671

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690

This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672

This theorem is referenced by:  19.40  1739  spsbe  1809  rexex  2843  ceqsexv2d  3071  imassrn  5185  fv3  5892  finacn  8499  dfac4  8571  kmlem2  8599  ac6c5  8930  ac6s3  8935  ac6s5  8939  bj-finsumval0  31772  mptsnunlem  31810  topdifinffinlem  31820  heiborlem3  32209  ac6s3f  32478