ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  2false Unicode version

Theorem 2false 653
Description: Two falsehoods are equivalent. (Contributed by NM, 4-Apr-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypotheses
Ref Expression
2false.1  |-  -.  ph
2false.2  |-  -.  ps
Assertion
Ref Expression
2false  |-  ( ph  <->  ps )

Proof of Theorem 2false
StepHypRef Expression
1 2false.1 . . 3  |-  -.  ph
21pm2.21i 611 . 2  |-  ( ph  ->  ps )
3 2false.2 . . 3  |-  -.  ps
43pm2.21i 611 . 2  |-  ( ps 
->  ph )
52, 4impbii 125 1  |-  ( ph  <->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 106  ax-ia3 107  ax-in2 581
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  bianfi  894  bifal  1303  dfnul2  3289  dfnul3  3290  rab0  3315  iun0  3792  0iun  3793  0xp  4531  cnv0  4848  co02  4957  0er  6340  bdnth  11998  bdnthALT  11999
  Copyright terms: Public domain W3C validator