MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  notnot1 Unicode version

Theorem notnot1 116
Description: Converse of double negation. Theorem *2.12 of [WhiteheadRussell] p. 101. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 2-Mar-2013.)
Assertion
Ref Expression
notnot1  |-  ( ph  ->  -.  -.  ph )

Proof of Theorem notnot1
StepHypRef Expression
1 id 21 . 2  |-  ( -. 
ph  ->  -.  ph )
21con2i 114 1  |-  ( ph  ->  -.  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6
This theorem is referenced by:  notnoti  117  con1d  118  con4i  124  notnot  284  biortn  397  pm2.13  409  eueq2  2940  ifnot  3604  eupath2  23308  stoweidlem39  27187  atbiffatnnbalt  27262  vk15.4j  27562  zfregs2VD  27885  vk15.4jVD  27958  con3ALTVD  27960
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
  Copyright terms: Public domain W3C validator