Theorem exancom 1054

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 1051	1 |- (E.x(ph /\ ps) <-> E.x(ps /\ ph))

Syntax hints:   <-> wb 146   /\ wa 223  E.wex 980

This theorem is referenced by:  19.29r 1072  19.42 1096  exan 1106  risset 1685  pwpw0 2469  pwsnALT 2501  dfuni2 2505  eluni2 2507  unipr 2515  dfiun2g 2586  uniuni 2880  imadif 3574  tz6.12-1 3736  ssxr 5540  grothinf 8781  chcmh 9113

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

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