Theorem exancom 1586

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 437	. 2 |- ((ph /\ ps) <-> (ps /\ ph))
2	1	exbii 1582	1 |- (E.x(ph /\ ps) <-> E.x(ps /\ ph))

Syntax hints:   <-> wb 176   /\ wa 358  E.wex 1541

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by:  19.29r  1597  19.42  1880  risset  2661  morex  3020  pwpw0  3855  pwsnALT  3882  dfuni2  3893  eluni2  3895  unipr  3905  dfiun2g  3999  dfimak2  4298  insklem  4304  el1st  4729  setconslem6  4736  dfcnv2  5100  imadif  5171  addcfnex  5824  addccan2nclem1  6263