Theorem exsimpr 1641

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 110	. 2 |- ( ( ph /\ ps ) -> ps )
2	1	eximi 1623	1 |- ( E. x ( ph /\ ps ) -> E. x ps )

Syntax hints:   -> wi 4   /\ wa 104   E.wex 1515

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-ial 1557

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  cbvexv1  1775  onm  4449  imassrn  5034  eliotaeu  5261  fv3  5601  relelfvdm  5610  nfvres  5612  brtpos2  6339  finacn  7318  cc1  7379  acnccim  7386  omiunct  12848