Theorem wl-mps

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

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

Proof

Step	Hyp	Ref	Expression
1		wl-mps.1	|- ( ph -> ( ps -> ch ) )
2		wl-mps.2	|- ( ( ph -> ch ) -> th )
3	1	a2i	|- ( ( ph -> ps ) -> ( ph -> ch ) )
4	3 2	syl	|- ( ( ph -> ps ) -> th )