Axiom ax-frege2

Description: If a proposition ch is a necessary consequence of two propositions ps and ph and one of those, ps , is in turn a necessary consequence of the other, ph , then the proposition ch is a necessary consequence of the latter one, ph , alone. Axiom 2 of Frege1879 p. 26. Identical to ax-2 . (Contributed by RP, 24-Dec-2019) (New usage is discouraged.)

	Ref	Expression
Assertion	ax-frege2	|- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> 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 1	wi	|- ( ph -> ps )
6	0 2	wi	|- ( ph -> ch )
7	5 6	wi	|- ( ( ph -> ps ) -> ( ph -> ch ) )
8	4 7	wi	|- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )