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 42331
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 42312, and ax-frege2 42313. (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 35222 1 wff ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))
Colors of variables: wff setvar class
This axiom is referenced by:  frege26  42332  frege9  42334  frege12  42335  frege10  42342  frege17  42343  frege38  42363  frege53aid  42381  frege53a  42382  frege62a  42402  frege66a  42406  frege53b  42412  frege62b  42429  frege66b  42433  frege53c  42436  frege62c  42447  frege66c  42451  frege74  42459  frege84  42469  frege96  42481
  Copyright terms: Public domain W3C validator