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

Theorem simprim 152
Description: Simplification. Similar to Theorem *3.27 (Simp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 13-Nov-2012.)
Assertion
Ref Expression
simprim  |-  ( -.  ( ph  ->  -.  ps )  ->  ps )

Proof of Theorem simprim
StepHypRef Expression
1 idd 25 . 2  |-  ( ph  ->  ( ps  ->  ps ) )
21impi 150 1  |-  ( -.  ( ph  ->  -.  ps )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  impt  159  impbi  188  biimpr  200  imbi12  322
  Copyright terms: Public domain W3C validator