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Theorem ifpbicor 39719
Description: Corollary of commutation of biimplication. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpbicor (if-(𝜑, 𝜓, ¬ 𝜓) ↔ if-(𝜓, 𝜑, ¬ 𝜑))

Proof of Theorem ifpbicor
StepHypRef Expression
1 bicom 223 . 2 ((𝜑𝜓) ↔ (𝜓𝜑))
2 ifpdfbi 39717 . 2 ((𝜑𝜓) ↔ if-(𝜑, 𝜓, ¬ 𝜓))
3 ifpdfbi 39717 . 2 ((𝜓𝜑) ↔ if-(𝜓, 𝜑, ¬ 𝜑))
41, 2, 33bitr3i 302 1 (if-(𝜑, 𝜓, ¬ 𝜓) ↔ if-(𝜓, 𝜑, ¬ 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  df-tru 1531
This theorem is referenced by:  ifpxorcor  39720
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