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Theorem bifal 1241
Description: A contradiction is equivalent to falsehood. (Contributed by Mario Carneiro, 9-May-2015.)
Hypothesis
Ref Expression
bifal.1 ¬ φ
Assertion
Ref Expression
bifal (φ ↔ ⊥ )

Proof of Theorem bifal
StepHypRef Expression
1 bifal.1 . 2 ¬ φ
2 fal 1235 . 2 ¬ ⊥
31, 22false 604 1 (φ ↔ ⊥ )
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98  wfal 1233
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-fal 1234
This theorem is referenced by: (None)
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