MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  notnot2 Structured version   Unicode version

Theorem notnot2 106
Description: Converse of double negation. Theorem *2.14 of [WhiteheadRussell] p. 102. (Contributed by NM, 5-Aug-1993.) (Proof shortened by David Harvey, 5-Sep-1999.) (Proof shortened by Josh Purinton, 29-Dec-2000.)
Assertion
Ref Expression
notnot2  |-  ( -. 
-.  ph  ->  ph )

Proof of Theorem notnot2
StepHypRef Expression
1 pm2.21 102 . 2  |-  ( -. 
-.  ph  ->  ( -. 
ph  ->  ph ) )
21pm2.18d 105 1  |-  ( -. 
-.  ph  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  notnotrd  107  notnotri  108  con2d  109  con3d  127  notnot  283  ecase3ad  912  con3ALT  28614  zfregs2VD  28953  con3ALTVD  29028  notnot2ALT2  29039
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
  Copyright terms: Public domain W3C validator