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Theorem frege7 36925
Description: A closed form of syl6 34. The first antecedent is used to replace the consequent of the second antecedent. Proposition 7 of [Frege1879] p. 34. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege7 ((𝜑𝜓) → ((𝜒 → (𝜃𝜑)) → (𝜒 → (𝜃𝜓))))

Proof of Theorem frege7
StepHypRef Expression
1 frege5 36917 . 2 ((𝜑𝜓) → ((𝜃𝜑) → (𝜃𝜓)))
2 frege6 36923 . 2 (((𝜑𝜓) → ((𝜃𝜑) → (𝜃𝜓))) → ((𝜑𝜓) → ((𝜒 → (𝜃𝜑)) → (𝜒 → (𝜃𝜓)))))
31, 2ax-mp 5 1 ((𝜑𝜓) → ((𝜒 → (𝜃𝜑)) → (𝜒 → (𝜃𝜓))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36907  ax-frege2 36908
This theorem is referenced by:  frege32  36952  frege67a  37002  frege67b  37029  frege67c  37047  frege94  37074  frege107  37087  frege113  37093
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