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Theorem bianfd 866
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 852 . 2 (𝜑 → ¬ (𝜓𝜒))
31, 22falsed 628 1 (𝜑 → (𝜓 ↔ (𝜓𝜒)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  eueq2dc  2737  eueq3dc  2738
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