MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm3.45 Unicode version

Theorem pm3.45 807
Description: Theorem *3.45 (Fact) of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm3.45  |-  ( (
ph  ->  ps )  -> 
( ( ph  /\  ch )  ->  ( ps 
/\  ch ) ) )

Proof of Theorem pm3.45
StepHypRef Expression
1 id 19 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21anim1d 547 1  |-  ( (
ph  ->  ps )  -> 
( ( ph  /\  ch )  ->  ( ps 
/\  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  rabss2  3269  lmcnp  17048  fbflim2  17688  ivthlem2  18828  ivthlem3  18829  ssrmo  23164  arg-ax  24927  pm10.56  27668
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