Theorem exsimpl 1553

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 107	. 2 |- ( ( ph /\ ps ) -> ph )
2	1	eximi 1536	1 |- ( E. x ( ph /\ ps ) -> E. x ph )

Syntax hints:   -> wi 4   /\ wa 102   E.wex 1426

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  19.40  1567  euex  1978  moexexdc  2032  elex  2630  sbc5  2863  dmcoss  4702  fmptco  5464  brabvv  5695  brtpos2  6016