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Theorem mt2bi 642
Description: A false consequent falsifies an antecedent. (Contributed by NM, 19-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Nov-2012.)
Hypothesis
Ref Expression
mt2bi.1 𝜑
Assertion
Ref Expression
mt2bi 𝜓 ↔ (𝜓 → ¬ 𝜑))

Proof of Theorem mt2bi
StepHypRef Expression
1 mt2bi.1 . . 3 𝜑
21a1bi 241 . 2 𝜓 ↔ (𝜑 → ¬ 𝜓))
3 con2b 626 . 2 ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))
42, 3bitri 182 1 𝜓 ↔ (𝜓 → ¬ 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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