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Theorem ifpnotnotb 38608
Description: Factor conditional logic operator over negation in terms 2 and 3. (Contributed by RP, 21-Apr-2020.)
Assertion
Ref Expression
ifpnotnotb (if-(𝜑, ¬ 𝜓, ¬ 𝜒) ↔ ¬ if-(𝜑, 𝜓, 𝜒))

Proof of Theorem ifpnotnotb
StepHypRef Expression
1 ifpnot23 38607 . 2 (¬ if-(𝜑, 𝜓, 𝜒) ↔ if-(𝜑, ¬ 𝜓, ¬ 𝜒))
21bicomi 216 1 (if-(𝜑, ¬ 𝜓, ¬ 𝜒) ↔ ¬ if-(𝜑, 𝜓, 𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 198  if-wif 1086
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 199  df-an 386  df-or 875  df-ifp 1087
This theorem is referenced by:  ifpananb  38635  ifpnannanb  38636  ifpxorxorb  38640
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