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Theorem ifpbicor 38322
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 212 . 2 ((𝜑𝜓) ↔ (𝜓𝜑))
2 ifpdfbi 38320 . 2 ((𝜑𝜓) ↔ if-(𝜑, 𝜓, ¬ 𝜓))
3 ifpdfbi 38320 . 2 ((𝜓𝜑) ↔ if-(𝜓, 𝜑, ¬ 𝜑))
41, 2, 33bitr3i 290 1 (if-(𝜑, 𝜓, ¬ 𝜓) ↔ if-(𝜓, 𝜑, ¬ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  if-wif 1050
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-or 384  df-an 385  df-ifp 1051  df-tru 1635
This theorem is referenced by:  ifpxorcor  38323
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