Theorem wl-syls2

Description: Replacing a nested antecedent. A sort of syllogism in antecedent position. (Contributed by Wolf Lammen, 20-Sep-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	wl-syls2.1	|- ( ph -> ps )
	wl-syls2.2	|- ( ( ph -> ch ) -> th )
Assertion	wl-syls2	|- ( ( ps -> ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		wl-syls2.1	|- ( ph -> ps )
2		wl-syls2.2	|- ( ( ph -> ch ) -> th )
3	1	imim1i	|- ( ( ps -> ch ) -> ( ph -> ch ) )
4	3 2	syl	|- ( ( ps -> ch ) -> th )