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Theorem frege58acor 37190
Description: Lemma for frege59a 37191. (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 37189 . 2 (((𝜓𝜒) ∧ (𝜃𝜏)) → if-(𝜑, (𝜓𝜒), (𝜃𝜏)))
2 ifpimim 36873 . 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 383  if-wif 1006
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege58a 37189
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-ifp 1007
This theorem is referenced by:  frege59a  37191  frege60a  37192  frege62a  37194
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