MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.04 Unicode version

Theorem pm2.04 78
Description: Swap antecedents. Theorem *2.04 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Sep-2012.)
Assertion
Ref Expression
pm2.04  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ps  ->  ( ph  ->  ch ) ) )

Proof of Theorem pm2.04
StepHypRef Expression
1 id 21 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ph  ->  ( ps  ->  ch ) ) )
21com23 74 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ps  ->  ( ph  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6
This theorem is referenced by:  com34  79  com45  85  bi2.04  352  merco2  1496  ralcom3  2680  rexrsb  27296  syl5imp  27410  com3rgbi  27412  syl5impVD  27772  simplbi2comgVD  27797  19.41rgVD  27811  a9e2eqVD  27816
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-mp 10
  Copyright terms: Public domain W3C validator