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

Theorem pm3.3 444
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 22 . 2  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ( ph  /\  ps )  ->  ch )
)
21expd 436 1  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ph  ->  ( ps 
->  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  impexp  446  pm4.79  583  mo3OLD  2325  wl-mo3t  30226  trer  30339  trsbc  33454  simplbi2VD  33789  exbirVD  33796  exbiriVD  33797  3impexpVD  33799  trsbcVD  33820  simplbi2comtVD  33831  bj-alanim  34347
  Copyright terms: Public domain W3C validator