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Theorem axfrege52a 37047
Description: Justification for ax-frege52a 37048. (Contributed by RP, 17-Apr-2020.)
Assertion
Ref Expression
axfrege52a ((𝜑𝜓) → (if-(𝜑, 𝜃, 𝜒) → if-(𝜓, 𝜃, 𝜒)))

Proof of Theorem axfrege52a
StepHypRef Expression
1 ifpbi1 36718 . 2 ((𝜑𝜓) → (if-(𝜑, 𝜃, 𝜒) ↔ if-(𝜓, 𝜃, 𝜒)))
21biimpd 217 1 ((𝜑𝜓) → (if-(𝜑, 𝜃, 𝜒) → if-(𝜓, 𝜃, 𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  if-wif 1005
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 195  df-or 383  df-an 384  df-ifp 1006
This theorem is referenced by: (None)
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