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Theorem exancom 1588
Description: Commutation of conjunction inside an existential quantifier. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
exancom  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )

Proof of Theorem exancom
StepHypRef Expression
1 ancom 264 . 2  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ph )
)
21exbii 1585 1  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104   E.wex 1469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-ial 1515
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  19.29r  1601  19.42h  1666  19.42  1667  risset  2464  morex  2869  dfuni2  3742  eluni2  3744  unipr  3754  dfiun2g  3849  uniuni  4376  cnvco  4728  imadif  5207  funimaexglem  5210  bdcuni  13228  bj-axun2  13267
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