Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege24 Structured version   Visualization version   GIF version

Theorem frege24 42175
Description: Closed form for a1d 25. Deduction introducing an embedded antecedent. Identical to rp-frege24 42157 which was proved without relying on ax-frege8 42169. Proposition 24 of [Frege1879] p. 42. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege24 ((𝜑𝜓) → (𝜑 → (𝜒𝜓)))

Proof of Theorem frege24
StepHypRef Expression
1 ax-frege1 42150 . 2 ((𝜑𝜓) → (𝜒 → (𝜑𝜓)))
2 frege12 42173 . 2 (((𝜑𝜓) → (𝜒 → (𝜑𝜓))) → ((𝜑𝜓) → (𝜑 → (𝜒𝜓))))
31, 2ax-mp 5 1 ((𝜑𝜓) → (𝜑 → (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 42150  ax-frege2 42151  ax-frege8 42169
This theorem is referenced by:  frege25  42177  frege63a  42241  frege63b  42268  frege63c  42286
  Copyright terms: Public domain W3C validator