Axiom ax-frege8 43833

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 43814, and ax-frege2 43815. (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 36560	1 wff ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

This axiom is referenced by:  frege26  43834  frege9  43836  frege12  43837  frege10  43844  frege17  43845  frege38  43865  frege53aid  43883  frege53a  43884  frege62a  43904  frege66a  43908  frege53b  43914  frege62b  43931  frege66b  43935  frege53c  43938  frege62c  43949  frege66c  43953  frege74  43961  frege84  43971  frege96  43983