MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.61 Unicode version

Theorem pm2.61 163
Description: Theorem *2.61 of [WhiteheadRussell] p. 107. Useful for eliminating an antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 22-Sep-2013.)
Assertion
Ref Expression
pm2.61  |-  ( (
ph  ->  ps )  -> 
( ( -.  ph  ->  ps )  ->  ps ) )

Proof of Theorem pm2.61
StepHypRef Expression
1 pm2.6 162 . 2  |-  ( ( -.  ph  ->  ps )  ->  ( ( ph  ->  ps )  ->  ps )
)
21com12 27 1  |-  ( (
ph  ->  ps )  -> 
( ( -.  ph  ->  ps )  ->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  onfrALT  28613  onfrALTVD  28983  bnj1109  29134  isltrn2N  30931  ltrnid  30946  ltrneq  30960
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
  Copyright terms: Public domain W3C validator