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Theorem frege19 42076
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 42064 . 2 ((𝜓𝜒) → ((𝜒𝜃) → (𝜓𝜃)))
2 frege18 42070 . 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 42042  ax-frege2 42043  ax-frege8 42061
This theorem is referenced by:  frege21  42079  frege20  42080  frege71  42186  frege86  42201  frege103  42218  frege119  42234  frege123  42238
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