MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm3.3 Unicode version

Theorem pm3.3 432
Description: Theorem *3.3 (Exp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)
Assertion
Ref Expression
pm3.3  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ph  ->  ( ps 
->  ch ) ) )

Proof of Theorem pm3.3
StepHypRef Expression
1 id 20 . 2  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ( ph  /\  ps )  ->  ch )
)
21exp3a 426 1  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ph  ->  ( ps 
->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  impexp  434  pm4.79  567  trer  26010  trsbc  27968  simplbi2VD  28299  exbirVD  28306  exbiriVD  28307  3impexpVD  28309  trsbcVD  28330  simplbi2comgVD  28341
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