Theorem exsimpl 1628

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 109	. 2 |- ( ( ph /\ ps ) -> ph )
2	1	eximi 1611	1 |- ( E. x ( ph /\ ps ) -> E. x ph )

Syntax hints:   -> wi 4   /\ wa 104   E.wex 1503

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.40  1642  euex  2072  moexexdc  2126  elex  2771  sbc5  3009  dmcoss  4931  fmptco  5724  brabvv  5964  brtpos2  6304