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Theorem 2false 348
Description: Two falsehoods are equivalent. (Contributed by NM, 4-Apr-2005.) (Proof shortened by Wolf Lammen, 19-May-2013.)
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
2 2false.2 . . 3  |-  -.  ps
31, 22th 239 . 2  |-  ( -. 
ph 
<->  -.  ps )
43con4bii 295 1  |-  ( ph  <->  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185
This theorem is referenced by:  bianfi  926  bifal  1418  iun0  4326  0iun  4327  sbcbr  4446  0xp  4903  cnv0  5226  co02  5336  0er  7382  00lss  17906  00ply1bas  18599  signswch  29010  pexmidlem8N  32974  dandysum2p2e4  37519
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