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Theorem frege19 37635
Description: A closed form of syl6 35. Proposition 19 of [Frege1879] p. 39. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege19 ((𝜑 → (𝜓𝜒)) → ((𝜒𝜃) → (𝜑 → (𝜓𝜃))))

Proof of Theorem frege19
StepHypRef Expression
1 frege9 37623 . 2 ((𝜓𝜒) → ((𝜒𝜃) → (𝜓𝜃)))
2 frege18 37629 . 2 (((𝜓𝜒) → ((𝜒𝜃) → (𝜓𝜃))) → ((𝜑 → (𝜓𝜒)) → ((𝜒𝜃) → (𝜑 → (𝜓𝜃)))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓𝜒)) → ((𝜒𝜃) → (𝜑 → (𝜓𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 37601  ax-frege2 37602  ax-frege8 37620
This theorem is referenced by:  frege21  37638  frege20  37639  frege71  37745  frege86  37760  frege103  37777  frege119  37793  frege123  37797
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