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Theorem 2false 339
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 230 . 2 φ ↔ ¬ ψ)
43con4bii 288 1 (φψ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176
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 177
This theorem is referenced by:  bianfi  891  bifal  1327  iun0  4022  0iun  4023  xp0r  4842  cnv0  5031  co02  5092
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