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Theorem exancom 1540
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 262 . 2  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ph )
)
21exbii 1537 1  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  19.29r  1553  19.42h  1618  19.42  1619  risset  2395  morex  2777  dfuni2  3611  eluni2  3613  unipr  3623  dfiun2g  3718  uniuni  4209  cnvco  4548  imadif  5010  funimaexglem  5013  bdcuni  10825  bj-axun2  10864
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