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Theorem frege68a 36996
Description: Combination of applying a definition and applying it to a specific instance. Proposition 68 of [Frege1879] p. 54. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege68a (((𝜓𝜒) ↔ 𝜃) → (𝜃 → if-(𝜑, 𝜓, 𝜒)))

Proof of Theorem frege68a
StepHypRef Expression
1 frege57aid 36982 . 2 (((𝜓𝜒) ↔ 𝜃) → (𝜃 → (𝜓𝜒)))
2 frege67a 36995 . 2 ((((𝜓𝜒) ↔ 𝜃) → (𝜃 → (𝜓𝜒))) → (((𝜓𝜒) ↔ 𝜃) → (𝜃 → if-(𝜑, 𝜓, 𝜒))))
31, 2ax-mp 5 1 (((𝜓𝜒) ↔ 𝜃) → (𝜃 → if-(𝜑, 𝜓, 𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  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-frege52a 36967  ax-frege58a 36985
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-ifp 1006  df-tru 1477  df-fal 1480
This theorem is referenced by: (None)
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