Theorem exancom 1568

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

Step	Hyp	Ref	Expression
1		ancom 264	. 2 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
2	1	exbii 1565	1 |- ( E. x ( ph /\ ps ) <-> E. x ( ps /\ ph ) )

Syntax hints:   /\ wa 103   <-> wb 104   E.wex 1449

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1404  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-4 1468  ax-ial 1495

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  19.29r  1581  19.42h  1646  19.42  1647  risset  2435  morex  2835  dfuni2  3702  eluni2  3704  unipr  3714  dfiun2g  3809  uniuni  4330  cnvco  4682  imadif  5159  funimaexglem  5162  bdcuni  12757  bj-axun2  12796