Axiom ax-frege8 40162

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 40143, and ax-frege2 40144. (Redundant) Axiom 8 of [Frege1879] p. 35. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-frege8	⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

Detailed syntax breakdown of Axiom ax-frege8

Step	Hyp	Ref	Expression
1		wph	. 2 wff 𝜑
2		wps	. . 3 wff 𝜓
3		wch	. . 3 wff 𝜒
4	2, 3	wi 4	. 2 wff (𝜓 → 𝜒)
5	1, 3	wi 4	. . 3 wff (𝜑 → 𝜒)
6	2, 5	wi 4	. 2 wff (𝜓 → (𝜑 → 𝜒))
7	1, 4, 6	bj-0 33883	1 wff ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

This axiom is referenced by:  frege26  40163  frege9  40165  frege12  40166  frege10  40173  frege17  40174  frege38  40194  frege53aid  40212  frege53a  40213  frege62a  40233  frege66a  40237  frege53b  40243  frege62b  40260  frege66b  40264  frege53c  40267  frege62c  40278  frege66c  40282  frege74  40290  frege84  40300  frege96  40312