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Theorem ifporcor 37326
Description: Corollary of commutation of or. (Contributed by RP, 20-Apr-2020.)
Assertion
Ref Expression
ifporcor (if-(𝜑, 𝜑, 𝜓) ↔ if-(𝜓, 𝜓, 𝜑))

Proof of Theorem ifporcor
StepHypRef Expression
1 orcom 402 . 2 ((𝜑𝜓) ↔ (𝜓𝜑))
2 ifpdfor2 37325 . 2 ((𝜑𝜓) ↔ if-(𝜑, 𝜑, 𝜓))
3 ifpdfor2 37325 . 2 ((𝜓𝜑) ↔ if-(𝜓, 𝜓, 𝜑))
41, 2, 33bitr3i 290 1 (if-(𝜑, 𝜑, 𝜓) ↔ if-(𝜓, 𝜓, 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wo 383  if-wif 1011
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 385  df-an 386  df-ifp 1012
This theorem is referenced by:  ifpnorcor  37345
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