Theorem exsimpr 1671

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 1653	1 |- ( E. x ( ph /\ ps ) -> E. x ps )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   E.wex 1545

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-ial 1587

This proof depends on definitions:  df-bi 117

This theorem is used by:  cbvexv1  1805  onm  4548  imassrn  5140  eliotaeu  5369  fv3  5721  relelfvdm  5730  nfvres  5735  brtpos2  6526  finacn  7566  cc1  7637  acnccim  7644  omiunct  13393