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Theorem frege66a 36994
Description: Swap antecedents of frege65a 36993. 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 36993 . 2 (((𝜓𝜒) ∧ (𝜏𝜂)) → (((𝜒𝜃) ∧ (𝜂𝜁)) → (if-(𝜑, 𝜓, 𝜏) → if-(𝜑, 𝜃, 𝜁))))
2 ax-frege8 36919 . 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 382  if-wif 1005
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege1 36900  ax-frege2 36901  ax-frege8 36919  ax-frege58a 36985
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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