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 37923
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 37904, and ax-frege2 37905. (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 32508 1 wff ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))
Colors of variables: wff setvar class
This axiom is referenced by:  frege26  37924  frege9  37926  frege12  37927  frege10  37934  frege17  37935  frege38  37955  frege53aid  37973  frege53a  37974  frege62a  37994  frege66a  37998  frege53b  38004  frege62b  38021  frege66b  38025  frege53c  38028  frege62c  38039  frege66c  38043  frege74  38051  frege84  38061  frege96  38073
  Copyright terms: Public domain W3C validator