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Theorem 2false 673
Description: Two falsehoods are equivalent. (Contributed by NM, 4-Apr-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
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
21pm2.21i 618 . 2 (𝜑𝜓)
3 2false.2 . . 3 ¬ 𝜓
43pm2.21i 618 . 2 (𝜓𝜑)
52, 4impbii 125 1 (𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107  ax-in2 587
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  bianfi  914  bifal  1327  dfnul2  3333  dfnul3  3334  rab0  3359  iun0  3837  0iun  3838  0xp  4587  cnv0  4910  co02  5020  0er  6429  bdnth  12834  bdnthALT  12835
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