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Theorem frege49 38641
Description: Closed form of deduction with disjunction. Proposition 49 of [Frege1879] p. 49. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege49 ((¬ 𝜑𝜓) → ((𝜑𝜒) → ((𝜓𝜒) → 𝜒)))

Proof of Theorem frege49
StepHypRef Expression
1 frege47 38639 . 2 ((¬ 𝜑𝜓) → ((𝜓𝜒) → ((𝜑𝜒) → 𝜒)))
2 frege12 38601 . 2 (((¬ 𝜑𝜓) → ((𝜓𝜒) → ((𝜑𝜒) → 𝜒))) → ((¬ 𝜑𝜓) → ((𝜑𝜒) → ((𝜓𝜒) → 𝜒))))
31, 2ax-mp 5 1 ((¬ 𝜑𝜓) → ((𝜑𝜒) → ((𝜓𝜒) → 𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 38578  ax-frege2 38579  ax-frege8 38597  ax-frege28 38618  ax-frege31 38622  ax-frege41 38633
This theorem is referenced by:  frege50  38642
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