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Theorem ifpnorcor 39724
Description: Corollary of commutation of nor. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpnorcor (if-(𝜑, ¬ 𝜑, ¬ 𝜓) ↔ if-(𝜓, ¬ 𝜓, ¬ 𝜑))

Proof of Theorem ifpnorcor
StepHypRef Expression
1 ifporcor 39705 . . 3 (if-(𝜑, 𝜑, 𝜓) ↔ if-(𝜓, 𝜓, 𝜑))
21notbii 321 . 2 (¬ if-(𝜑, 𝜑, 𝜓) ↔ ¬ if-(𝜓, 𝜓, 𝜑))
3 ifpnot23 39722 . 2 (¬ if-(𝜑, 𝜑, 𝜓) ↔ if-(𝜑, ¬ 𝜑, ¬ 𝜓))
4 ifpnot23 39722 . 2 (¬ if-(𝜓, 𝜓, 𝜑) ↔ if-(𝜓, ¬ 𝜓, ¬ 𝜑))
52, 3, 43bitr3i 302 1 (if-(𝜑, ¬ 𝜑, ¬ 𝜓) ↔ if-(𝜓, ¬ 𝜓, ¬ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 207  if-wif 1054
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 208  df-an 397  df-or 842  df-ifp 1055
This theorem is referenced by: (None)
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