Theorem exancom 1661

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 1658	1 |- ( E. x ( ph /\ ps ) <-> E. x ( ps /\ ph ) )

Syntax hints:   /\ wa 104   <-> wb 105   E.wex 1545

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-ial 1587

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.29r  1674  19.42h  1739  19.42  1740  risset  2578  morex  3010  dfuni2  3932  eluni2  3934  unipr  3944  dfiun2g  4039  uniuni  4592  cnvco  4960  imadif  5456  funimaexglem  5459  pceu  13052  bdcuni  16816  bj-axun2  16855