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Theorem bianfd 894
Description: A wff conjoined with falsehood is false. (Contributed by NM, 27-Mar-1995.) (Proof shortened by Wolf Lammen, 5-Nov-2013.)
Hypothesis
Ref Expression
bianfd.1 (𝜑 → ¬ 𝜓)
Assertion
Ref Expression
bianfd (𝜑 → (𝜓 ↔ (𝜓𝜒)))

Proof of Theorem bianfd
StepHypRef Expression
1 bianfd.1 . 2 (𝜑 → ¬ 𝜓)
21intnanrd 879 . 2 (𝜑 → ¬ (𝜓𝜒))
31, 22falsed 653 1 (𝜑 → (𝜓 ↔ (𝜓𝜒)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 102  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 579  ax-in2 580
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  eueq2dc  2788  eueq3dc  2789
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