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Theorem ninba 985
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 984 . 2 𝜓 → ((𝜒𝜓) ↔ ¬ 𝜑))
32bicomd 213 1 𝜓 → (¬ 𝜑 ↔ (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wa 383
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 385
This theorem is referenced by: (None)
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