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Theorem 2false 377
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 265 . 2 𝜑 ↔ ¬ 𝜓)
43con4bii 322 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 207
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 208
This theorem is referenced by:  bianfi  534  bifal  1544  dfnul2  4290  co02  6106  0er  8315  00lss  19642  00ply1bas  20336  2lgslem4  25909  signswch  31730  pexmidlem8N  36993  dandysum2p2e4  43111
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