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Theorem bianfi 891
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 ↔ (ψ φ))

Proof of Theorem bianfi
StepHypRef Expression
1 bianfi.1 . 2 ¬ φ
21intnan 880 . 2 ¬ (ψ φ)
31, 22false 339 1 (φ ↔ (ψ φ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176   wa 358
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 177  df-an 360
This theorem is referenced by:  in0  3576
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