MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm3.21 Unicode version

Theorem pm3.21 437
Description: Join antecedents with conjunction. Theorem *3.21 of [WhiteheadRussell] p. 111. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
pm3.21  |-  ( ph  ->  ( ps  ->  ( ps  /\  ph ) ) )

Proof of Theorem pm3.21
StepHypRef Expression
1 pm3.2 436 . 2  |-  ( ps 
->  ( ph  ->  ( ps  /\  ph ) ) )
21com12 29 1  |-  ( ph  ->  ( ps  ->  ( ps  /\  ph ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    /\ wa 360
This theorem is referenced by:  pm3.22  438  iba  491  ancr  534  anc2r  541  pm5.31  574  19.41  1819  2mo  2222  smoord  6377  fisupg  7100  winalim2  8313  aalioulem5  19710  musum  20425  chrelat2i  22937  relin01  23492  waj-ax  24260  sssu  24540  pm11.71  26995  onfrALTlem2  27582  19.41rg  27587  onfrALTlem2VD  27933  2pm13.193VD  27947  a9e2eqVD  27951  bnj1173  28299  hlrelat2  28859
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
  Copyright terms: Public domain W3C validator