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

Theorem pm3.45 808
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 20 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21anim1d 548 1  |-  ( (
ph  ->  ps )  -> 
( ( ph  /\  ch )  ->  ( ps 
/\  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  rabss2  3426  lmcnp  17368  fbflim2  18009  ivthlem2  19349  ivthlem3  19350  ssrmo  23981  arg-ax  26166  pm10.56  27542
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