Theorem exancom 1052

Description: Commutation of conjunction inside an existential quantifier.

Assertion

Ref	Expression
exancom	|- (E.x(ph /\ ps) <-> E.x(ps /\ ph))

Proof of Theorem exancom

Step	Hyp	Ref	Expression
1		ancom 435	. 2 |- ((ph /\ ps) <-> (ps /\ ph))
2	1	exbii 1049	1 |- (E.x(ph /\ ps) <-> E.x(ps /\ ph))

Syntax hints:   <-> wb 146   /\ wa 223  E.wex 978

This theorem is referenced by:  19.29r 1070  19.42 1094  exan 1104  risset 1682  pwpw0 2465  dfuni2 2500  eluni2 2502  unipr 2510  dfiun2g 2581  uniuni 2875  imadif 3566  tz6.12-1 3727  ssxr 5521  grothinf 8720  chcmh 9052

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-4 971  ax-5o 973

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979

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