Axiom ax-frege8 44808

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 91 which can be proved from only ax-mp 5, ax-frege1 44789, and ax-frege2 44790. (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 37408	1 wff ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

This axiom is used by:  frege26  44809  frege9  44811  frege12  44812  frege10  44819  frege17  44820  frege38  44840  frege53aid  44858  frege53a  44859  frege62a  44879  frege66a  44883  frege53b  44889  frege62b  44906  frege66b  44910  frege53c  44913  frege62c  44924  frege66c  44928  frege74  44936  frege84  44946  frege96  44958