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Theorem frege16 38604
Description: A closed form of com34 91. Proposition 16 of [Frege1879] p. 38. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege16 ((𝜑 → (𝜓 → (𝜒 → (𝜃𝜏)))) → (𝜑 → (𝜓 → (𝜃 → (𝜒𝜏)))))

Proof of Theorem frege16
StepHypRef Expression
1 frege12 38601 . 2 ((𝜓 → (𝜒 → (𝜃𝜏))) → (𝜓 → (𝜃 → (𝜒𝜏))))
2 frege5 38588 . 2 (((𝜓 → (𝜒 → (𝜃𝜏))) → (𝜓 → (𝜃 → (𝜒𝜏)))) → ((𝜑 → (𝜓 → (𝜒 → (𝜃𝜏)))) → (𝜑 → (𝜓 → (𝜃 → (𝜒𝜏))))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓 → (𝜒 → (𝜃𝜏)))) → (𝜑 → (𝜓 → (𝜃 → (𝜒𝜏)))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 38578  ax-frege2 38579  ax-frege8 38597
This theorem is referenced by:  frege18  38606  frege22  38607  frege17  38609
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