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Theorem frege6 36923
Description: A closed form of imim2d 54 which is a deduction adding nested antecedents. Proposition 6 of [Frege1879] p. 33. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege6 ((𝜑 → (𝜓𝜒)) → (𝜑 → ((𝜃𝜓) → (𝜃𝜒))))

Proof of Theorem frege6
StepHypRef Expression
1 frege5 36917 . 2 ((𝜓𝜒) → ((𝜃𝜓) → (𝜃𝜒)))
2 frege5 36917 . 2 (((𝜓𝜒) → ((𝜃𝜓) → (𝜃𝜒))) → ((𝜑 → (𝜓𝜒)) → (𝜑 → ((𝜃𝜓) → (𝜃𝜒)))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓𝜒)) → (𝜑 → ((𝜃𝜓) → (𝜃𝜒))))
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:  frege7  36925
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