Theorem exancom 1595

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 1592	1 |- ( E. x ( ph /\ ps ) <-> E. x ( ps /\ ph ) )

Syntax hints:   /\ wa 103   <-> wb 104   E.wex 1479

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 1434  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-4 1497  ax-ial 1521

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  19.29r  1608  19.42h  1674  19.42  1675  risset  2492  morex  2905  dfuni2  3785  eluni2  3787  unipr  3797  dfiun2g  3892  uniuni  4423  cnvco  4783  imadif  5262  funimaexglem  5265  pceu  12204  bdcuni  13593  bj-axun2  13632