Theorem exsimpl 1795

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 473	. 2 |- ( ( ph /\ ps ) -> ph )
2	1	eximi 1762	1 |- ( E. x ( ph /\ ps ) -> E. x ph )

Syntax hints:   -> wi 4   /\ wa 384   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  19.40  1797  euexALT  2511  moexex  2541  elex  3212  sbc5  3460  r19.2zb  4061  dmcoss  5385  suppimacnvss  7305  unblem2  8213  kmlem8  8979  isssc  16480  bnj1143  30861  bnj1371  31097  bnj1374  31099  bj-elissetv  32861  atex  34692  rtrclex  37924  clcnvlem  37930  pm10.55  38568