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Theorem frege4 40023
Description: Special case of closed form of a2d 29. Special case of rp-frege4g 40022. Proposition 4 of [Frege1879] p. 31. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege4 (((𝜑𝜓) → (𝜒 → (𝜑𝜓))) → ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓))))

Proof of Theorem frege4
StepHypRef Expression
1 frege3 40019 . 2 ((𝜑𝜓) → ((𝜒 → (𝜑𝜓)) → ((𝜒𝜑) → (𝜒𝜓))))
2 ax-frege2 40015 . 2 (((𝜑𝜓) → ((𝜒 → (𝜑𝜓)) → ((𝜒𝜑) → (𝜒𝜓)))) → (((𝜑𝜓) → (𝜒 → (𝜑𝜓))) → ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓)))))
31, 2ax-mp 5 1 (((𝜑𝜓) → (𝜒 → (𝜑𝜓))) → ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 40014  ax-frege2 40015
This theorem is referenced by:  frege5  40024
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