MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm3.33 Unicode version

Theorem pm3.33 568
Description: Theorem *3.33 (Syll) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm3.33  |-  ( ( ( ph  ->  ps )  /\  ( ps  ->  ch ) )  ->  ( ph  ->  ch ) )

Proof of Theorem pm3.33
StepHypRef Expression
1 imim1 70 . 2  |-  ( (
ph  ->  ps )  -> 
( ( ps  ->  ch )  ->  ( ph  ->  ch ) ) )
21imp 418 1  |-  ( ( ( ph  ->  ps )  /\  ( ps  ->  ch ) )  ->  ( ph  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  alsyl  1602  2sb5ndALT  28709  bnj1023  28812  bnj907  28997
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 177  df-an 360
  Copyright terms: Public domain W3C validator