Axiom ax-frege8 42203

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 42184, and ax-frege2 42185. (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 35081	1 wff ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

This axiom is referenced by:  frege26  42204  frege9  42206  frege12  42207  frege10  42214  frege17  42215  frege38  42235  frege53aid  42253  frege53a  42254  frege62a  42274  frege66a  42278  frege53b  42284  frege62b  42301  frege66b  42305  frege53c  42308  frege62c  42319  frege66c  42323  frege74  42331  frege84  42341  frege96  42353