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Theorem ifpancor 38306
Description: Corollary of commutation of and. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpancor (if-(𝜑, 𝜓, 𝜑) ↔ if-(𝜓, 𝜑, 𝜓))

Proof of Theorem ifpancor
StepHypRef Expression
1 ancom 465 . 2 ((𝜑𝜓) ↔ (𝜓𝜑))
2 ifpdfan2 38305 . 2 ((𝜑𝜓) ↔ if-(𝜑, 𝜓, 𝜑))
3 ifpdfan2 38305 . 2 ((𝜓𝜑) ↔ if-(𝜓, 𝜑, 𝜓))
41, 2, 33bitr3i 290 1 (if-(𝜑, 𝜓, 𝜑) ↔ if-(𝜓, 𝜑, 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 383  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
This theorem is referenced by:  ifpnancor  38324
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