Theorem wl-mps 33290

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.)

Hypotheses

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

Assertion

Ref	Expression
wl-mps	|- ( ( ph -> ps ) -> th )

Proof of Theorem wl-mps

Step	Hyp	Ref	Expression
1		wl-mps.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	a2i 14	. 2 |- ( ( ph -> ps ) -> ( ph -> ch ) )
3		wl-mps.2	. 2 |- ( ( ph -> ch ) -> th )
4	2, 3	syl 17	1 |- ( ( ph -> ps ) -> th )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  wl-syls1  33291