Theorem exsimpl 1508

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 102	. 2 |- ( ( ph /\ ps ) -> ph )
2	1	eximi 1491	1 |- ( E. x ( ph /\ ps ) -> E. x ph )

Syntax hints:   -> wi 4   /\ wa 97   E.wex 1381

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  19.40  1522  euex  1930  moexexdc  1984  elex  2566  sbc5  2787  dmcoss  4601  fmptco  5330  brabvv  5551  brtpos2  5866