Theorem exancom 1056

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 437	. 2 |- ((ph /\ ps) <-> (ps /\ ph))
2	1	exbii 1053	1 |- (E.x(ph /\ ps) <-> E.x(ps /\ ph))

Syntax hints:   <-> wb 146   /\ wa 223  E.wex 982

This theorem is referenced by:  19.29r 1074  19.42 1098  exan 1108  risset 1688  pwpw0 2473  pwsnALT 2505  dfuni2 2509  eluni2 2511  unipr 2519  dfiun2g 2590  uniuni 2886  imadif 3580  tz6.12-1 3742  ssxr 5552  grothinf 8776  chcmh 9108

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-4 975  ax-5o 977

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983

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