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Theorem niabn 885
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 107 . 2 ((𝜒𝜓) → 𝜓)
2 niabn.1 . . 3 𝜑
32pm2.24i 563 . 2 𝜑𝜓)
41, 3pm5.21ni 629 1 𝜓 → ((𝜒𝜓) ↔ ¬ 𝜑))
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-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  ninba  890
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