Axiom ax-frege8 43992

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 43973, and ax-frege2 43974. (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 36685	1 wff ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

This axiom is referenced by:  frege26  43993  frege9  43995  frege12  43996  frege10  44003  frege17  44004  frege38  44024  frege53aid  44042  frege53a  44043  frege62a  44063  frege66a  44067  frege53b  44073  frege62b  44090  frege66b  44094  frege53c  44097  frege62c  44108  frege66c  44112  frege74  44120  frege84  44130  frege96  44142