Theorem wl-syls1

Description: Replacing a nested consequent. 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-syls1.1	|- ( ps -> ch )
	wl-syls1.2	|- ( ( ph -> ch ) -> th )
Assertion	wl-syls1	|- ( ( ph -> ps ) -> th )

Proof

Step	Hyp	Ref	Expression
1		wl-syls1.1	|- ( ps -> ch )
2		wl-syls1.2	|- ( ( ph -> ch ) -> th )
3	1	a1i	|- ( ph -> ( ps -> ch ) )
4	3 2	wl-mps	|- ( ( ph -> ps ) -> th )