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Theorem bianfi 893
Description: A wff conjoined with falsehood is false. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)
Hypothesis
Ref Expression
bianfi.1 ¬ 𝜑
Assertion
Ref Expression
bianfi (𝜑 ↔ (𝜓𝜑))

Proof of Theorem bianfi
StepHypRef Expression
1 bianfi.1 . 2 ¬ 𝜑
21intnan 876 . 2 ¬ (𝜓𝜑)
31, 22false 652 1 (𝜑 ↔ (𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 102  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  in0  3317  opthprc  4489
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