Axiom ax-frege8

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 which can be proved from only ax-mp , ax-frege1 , and ax-frege2 . (Redundant) Axiom 8 of Frege1879 p. 35. (Contributed by RP, 24-Dec-2019) (New usage is discouraged.)

	Ref	Expression
Assertion	ax-frege8	|- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		wph	|- ph
1		wps	|- ps
2		wch	|- ch
3	1 2	wi	|- ( ps -> ch )
4	0 3	wi	|- ( ph -> ( ps -> ch ) )
5	0 2	wi	|- ( ph -> ch )
6	1 5	wi	|- ( ps -> ( ph -> ch ) )
7	4 6	wi	|- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) )