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Theorem niabn 963
Description: Miscellaneous inference relating falsehoods. (Contributed by NM, 31-Mar-1994.)
Hypothesis
Ref Expression
niabn.1 𝜑
Assertion
Ref Expression
niabn 𝜓 → ((𝜒𝜓) ↔ ¬ 𝜑))

Proof of Theorem niabn
StepHypRef Expression
1 simpr 477 . 2 ((𝜒𝜓) → 𝜓)
2 niabn.1 . . 3 𝜑
32pm2.24i 146 . 2 𝜑𝜓)
41, 3pm5.21ni 367 1 𝜓 → ((𝜒𝜓) ↔ ¬ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  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:  ninba  964
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