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Theorem frege58acor 37691
 Description: Lemma for frege59a 37692. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege58acor (((𝜓𝜒) ∧ (𝜃𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏)))

Proof of Theorem frege58acor
StepHypRef Expression
1 ax-frege58a 37690 . 2 (((𝜓𝜒) ∧ (𝜃𝜏)) → if-(𝜑, (𝜓𝜒), (𝜃𝜏)))
2 ifpimim 37374 . 2 (if-(𝜑, (𝜓𝜒), (𝜃𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏)))
31, 2syl 17 1 (((𝜓𝜒) ∧ (𝜃𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 384  if-wif 1011 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege58a 37690 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ifp 1012 This theorem is referenced by:  frege59a  37692  frege60a  37693  frege62a  37695
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