Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege7 Structured version   Visualization version   GIF version

Theorem frege7 38419
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 38411 . 2 ((𝜑𝜓) → ((𝜃𝜑) → (𝜃𝜓)))
2 frege6 38417 . 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 38401  ax-frege2 38402
This theorem is referenced by:  frege32  38446  frege67a  38496  frege67b  38523  frege67c  38541  frege94  38568  frege107  38581  frege113  38587
  Copyright terms: Public domain W3C validator