Theorem exancom 1606

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 266	. 2 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
2	1	exbii 1603	1 |- ( E. x ( ph /\ ps ) <-> E. x ( ps /\ ph ) )

Syntax hints:   /\ wa 104   <-> wb 105   E.wex 1490

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1445  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-4 1508  ax-ial 1532

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.29r  1619  19.42h  1685  19.42  1686  risset  2503  morex  2919  dfuni2  3807  eluni2  3809  unipr  3819  dfiun2g  3914  uniuni  4445  cnvco  4805  imadif  5288  funimaexglem  5291  pceu  12262  bdcuni  14188  bj-axun2  14227