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Theorem 2false 604
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 562 . 2 (φψ)
3 2false.2 . . 3 ¬ ψ
43pm2.21i 562 . 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 533
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  bianfi  847  bifal  1239  dfnul2  3204  dfnul3  3205  rab0  3224  iun0  3665  0iun  3666  0xp  4313  cnv0  4621  co02  4728
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