Theorem exsimpr 1667

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 1649	1 |- ( E. x ( ph /\ ps ) -> E. x ps )

Syntax hints:   -> wi 4   /\ wa 104   E.wex 1541

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-ial 1583

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  cbvexv1  1801  onm  4524  imassrn  5114  eliotaeu  5343  fv3  5695  relelfvdm  5704  nfvres  5708  brtpos2  6484  finacn  7513  cc1  7581  acnccim  7588  omiunct  13212