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Theorem ifpnancor 40773
Description: Corollary of commutation of and. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpnancor (if-(𝜑, ¬ 𝜓, ¬ 𝜑) ↔ if-(𝜓, ¬ 𝜑, ¬ 𝜓))

Proof of Theorem ifpnancor
StepHypRef Expression
1 ifpancor 40756 . . 3 (if-(𝜑, 𝜓, 𝜑) ↔ if-(𝜓, 𝜑, 𝜓))
21notbii 323 . 2 (¬ if-(𝜑, 𝜓, 𝜑) ↔ ¬ if-(𝜓, 𝜑, 𝜓))
3 ifpnot23 40770 . 2 (¬ if-(𝜑, 𝜓, 𝜑) ↔ if-(𝜑, ¬ 𝜓, ¬ 𝜑))
4 ifpnot23 40770 . 2 (¬ if-(𝜓, 𝜑, 𝜓) ↔ if-(𝜓, ¬ 𝜑, ¬ 𝜓))
52, 3, 43bitr3i 304 1 (if-(𝜑, ¬ 𝜓, ¬ 𝜑) ↔ if-(𝜓, ¬ 𝜑, ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 209  if-wif 1063
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 210  df-an 400  df-or 848  df-ifp 1064
This theorem is referenced by: (None)
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