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Theorem 2false 617
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 575 . 2 (𝜑𝜓)
3 2false.2 . . 3 ¬ 𝜓
43pm2.21i 575 . 2 (𝜓𝜑)
52, 4impbii 117 1 (𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101  ax-in2 545
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  bianfi  854  bifal  1256  dfnul2  3223  dfnul3  3224  rab0  3243  iun0  3710  0iun  3711  0xp  4383  cnv0  4690  co02  4797  0er  6103  bdnth  9803  bdnthALT  9804
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