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Theorem frege3 40493
Description: Add antecedent to ax-frege2 40489. Special case of rp-frege3g 40492. Proposition 3 of [Frege1879] p. 29. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege3 ((𝜑𝜓) → ((𝜒 → (𝜑𝜓)) → ((𝜒𝜑) → (𝜒𝜓))))

Proof of Theorem frege3
StepHypRef Expression
1 ax-frege2 40489 . 2 ((𝜒 → (𝜑𝜓)) → ((𝜒𝜑) → (𝜒𝜓)))
2 ax-frege1 40488 . 2 (((𝜒 → (𝜑𝜓)) → ((𝜒𝜑) → (𝜒𝜓))) → ((𝜑𝜓) → ((𝜒 → (𝜑𝜓)) → ((𝜒𝜑) → (𝜒𝜓)))))
31, 2ax-mp 5 1 ((𝜑𝜓) → ((𝜒 → (𝜑𝜓)) → ((𝜒𝜑) → (𝜒𝜓))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 40488  ax-frege2 40489
This theorem is referenced by:  frege4  40497
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