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Axiom ax-frege8 40161
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 40142, and ax-frege2 40143. (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 33885 1 wff ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))
Colors of variables: wff setvar class
This axiom is referenced by:  frege26  40162  frege9  40164  frege12  40165  frege10  40172  frege17  40173  frege38  40193  frege53aid  40211  frege53a  40212  frege62a  40232  frege66a  40236  frege53b  40242  frege62b  40259  frege66b  40263  frege53c  40266  frege62c  40277  frege66c  40281  frege74  40289  frege84  40299  frege96  40311
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