MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm3.22 Unicode version

Theorem pm3.22 437
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 pm3.21 436 . 2  |-  ( ph  ->  ( ps  ->  ( ps  /\  ph ) ) )
21imp 419 1  |-  ( (
ph  /\  ps )  ->  ( ps  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  ancom  438  ancom2s  778  ancom1s  781  eupickb  2345  brfi1uzind  11698  constr3lem4  21617  constr3trllem2  21621  constr3trllem3  21622  grpoidinvlem3  21777  atomli  23868  arg-ax  26109  cnambfre  26196  prter1  26660  3vfriswmgra  28151  1to2vfriswmgra  28152  frg2woteq  28205
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361
  Copyright terms: Public domain W3C validator