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Theorem frege66a 38495
 Description: Swap antecedents of frege65a 38494. Proposition 66 of [Frege1879] p. 54. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege66a (((𝜒𝜃) ∧ (𝜂𝜁)) → (((𝜓𝜒) ∧ (𝜏𝜂)) → (if-(𝜑, 𝜓, 𝜏) → if-(𝜑, 𝜃, 𝜁))))

Proof of Theorem frege66a
StepHypRef Expression
1 frege65a 38494 . 2 (((𝜓𝜒) ∧ (𝜏𝜂)) → (((𝜒𝜃) ∧ (𝜂𝜁)) → (if-(𝜑, 𝜓, 𝜏) → if-(𝜑, 𝜃, 𝜁))))
2 ax-frege8 38420 . 2 ((((𝜓𝜒) ∧ (𝜏𝜂)) → (((𝜒𝜃) ∧ (𝜂𝜁)) → (if-(𝜑, 𝜓, 𝜏) → if-(𝜑, 𝜃, 𝜁)))) → (((𝜒𝜃) ∧ (𝜂𝜁)) → (((𝜓𝜒) ∧ (𝜏𝜂)) → (if-(𝜑, 𝜓, 𝜏) → if-(𝜑, 𝜃, 𝜁)))))
31, 2ax-mp 5 1 (((𝜒𝜃) ∧ (𝜂𝜁)) → (((𝜓𝜒) ∧ (𝜏𝜂)) → (if-(𝜑, 𝜓, 𝜏) → if-(𝜑, 𝜃, 𝜁))))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383  if-wif 1032 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege1 38401  ax-frege2 38402  ax-frege8 38420  ax-frege58a 38486 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ifp 1033 This theorem is referenced by: (None)
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