Theorem exsimpl 1605

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
exsimpl	|- ( E. x ( ph /\ ps ) -> E. x ph )

Proof of Theorem exsimpl

Step	Hyp	Ref	Expression
1		simpl 108	. 2 |- ( ( ph /\ ps ) -> ph )
2	1	eximi 1588	1 |- ( E. x ( ph /\ ps ) -> E. x ph )

Syntax hints:   -> wi 4   /\ wa 103   E.wex 1480

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-ial 1522

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  19.40  1619  euex  2044  moexexdc  2098  elex  2737  sbc5  2974  dmcoss  4873  fmptco  5651  brabvv  5888  brtpos2  6219