Theorem exancom 1657

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 1654	1 |- ( E. x ( ph /\ ps ) <-> E. x ( ps /\ ph ) )

Syntax hints:   /\ wa 104   <-> wb 105   E.wex 1541

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-ial 1583

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.29r  1670  19.42h  1735  19.42  1736  risset  2561  morex  2991  dfuni2  3900  eluni2  3902  unipr  3912  dfiun2g  4007  uniuni  4554  cnvco  4921  imadif  5417  funimaexglem  5420  pceu  12948  bdcuni  16592  bj-axun2  16631