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Theorem pm3.22 449
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 pm3.21 448 . 2  |-  ( ph  ->  ( ps  ->  ( ps  /\  ph ) ) )
21imp 429 1  |-  ( (
ph  /\  ps )  ->  ( ps  /\  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  ancom  450  ancom2s  800  ancom1s  803  eupickbOLD  2345  brfi1uzind  12224  cshwlen  12441  cramerlem1  18498  cramer  18502  constr3lem4  23538  constr3trllem2  23542  constr3trllem3  23543  grpoidinvlem3  23698  atomli  25791  arg-ax  28267  cnambfre  28445  prter1  29029  clwwlkprop  30438  3vfriswmgra  30602  1to2vfriswmgra  30603  frg2woteq  30658  numclwwlkovfel2  30681  frgrareggt1  30714  pgrpgt2nabel  30774  mat1dimcrng  30878  dmatcrng  30886
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