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Theorem pm3.22 438
Description: Theorem *3.22 of [WhiteheadRussell] p. 111. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 13-Nov-2012.)
Assertion
Ref Expression
pm3.22  |-  ( (
ph  /\  ps )  ->  ( ps  /\  ph ) )

Proof of Theorem pm3.22
StepHypRef Expression
1 pm3.21 437 . 2  |-  ( ph  ->  ( ps  ->  ( ps  /\  ph ) ) )
21imp 420 1  |-  ( (
ph  /\  ps )  ->  ( ps  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    /\ wa 360
This theorem is referenced by:  ancom  439  ancom2s  780  ancom1s  783  eupickb  2178  grpoidinvlem3  20703  atomli  22792  arg-ax  24029  mapmapmap  24314  domrancur1c  24368  mslb1  24773  iintlem1  24776  pgapspf2  25219  prter1  25913
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
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