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Theorem ninba 916
Description: Miscellaneous inference relating falsehoods. (Contributed by NM, 31-Mar-1994.)
Hypothesis
Ref Expression
ninba.1 𝜑
Assertion
Ref Expression
ninba 𝜓 → (¬ 𝜑 ↔ (𝜒𝜓)))

Proof of Theorem ninba
StepHypRef Expression
1 ninba.1 . . 3 𝜑
21niabn 911 . 2 𝜓 → ((𝜒𝜓) ↔ ¬ 𝜑))
32bicomd 139 1 𝜓 → (¬ 𝜑 ↔ (𝜒𝜓)))
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 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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