Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ax-frege8 Structured version   Visualization version   GIF version

Axiom ax-frege8 38621
Description: Swap antecedents. If two conditions have a proposition as a consequence, their order is immaterial. Third axiom of Frege's 1879 work but identical to pm2.04 90 which can be proved from only ax-mp 5, ax-frege1 38602, and ax-frege2 38603. (Redundant) Axiom 8 of [Frege1879] p. 35. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.)
Assertion
Ref Expression
ax-frege8 ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))

Detailed syntax breakdown of Axiom ax-frege8
StepHypRef Expression
1 wph . 2 wff 𝜑
2 wps . . 3 wff 𝜓
3 wch . . 3 wff 𝜒
42, 3wi 4 . 2 wff (𝜓𝜒)
51, 3wi 4 . . 3 wff (𝜑𝜒)
62, 5wi 4 . 2 wff (𝜓 → (𝜑𝜒))
71, 4, 6bj-0 32872 1 wff ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))
Colors of variables: wff setvar class
This axiom is referenced by:  frege26  38622  frege9  38624  frege12  38625  frege10  38632  frege17  38633  frege38  38653  frege53aid  38671  frege53a  38672  frege62a  38692  frege66a  38696  frege53b  38702  frege62b  38719  frege66b  38723  frege53c  38726  frege62c  38737  frege66c  38741  frege74  38749  frege84  38759  frege96  38771
  Copyright terms: Public domain W3C validator