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Theorem 2false 364
Description: Two falsehoods are equivalent. (Contributed by NM, 4-Apr-2005.) (Proof shortened by Wolf Lammen, 19-May-2013.)
Hypotheses
Ref Expression
2false.1 ¬ 𝜑
2false.2 ¬ 𝜓
Assertion
Ref Expression
2false (𝜑𝜓)

Proof of Theorem 2false
StepHypRef Expression
1 2false.1 . . 3 ¬ 𝜑
2 2false.2 . . 3 ¬ 𝜓
31, 22th 254 . 2 𝜑 ↔ ¬ 𝜓)
43con4bii 310 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196
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 197
This theorem is referenced by:  bianfi  986  bifal  1537  cnv0OLD  5571  co02  5687  0er  7824  00lss  18990  00ply1bas  19658  2lgslem4  25176  signswch  30766  pexmidlem8N  35581  dandysum2p2e4  41486
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