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Theorem frege7 43109
Description: A closed form of syl6 35. 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 43101 . 2 ((𝜑𝜓) → ((𝜃𝜑) → (𝜃𝜓)))
2 frege6 43107 . 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 43091  ax-frege2 43092
This theorem is referenced by:  frege32  43136  frege67a  43186  frege67b  43213  frege67c  43231  frege94  43258  frege107  43271  frege113  43277
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