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Theorem bianfi 965
Description: A wff conjoined with falsehood is false. (Contributed by NM, 21-Jun-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 959 . 2 ¬ (𝜓𝜑)
31, 22false 365 1 (𝜑 ↔ (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wa 384
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 386
This theorem is referenced by:  in0  3942  opthprc  5129  ind1a  29876
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