Theorem wl-mpi 33252

Description: A nested modus ponens inference. Copy of mpi 20 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
wl-mpi	|- ( ph -> ch )

Proof of Theorem wl-mpi

Step	Hyp	Ref	Expression
1		wl-mpi.1	. . . 4 |- ps
2	1	wl-a1i 33251	. . 3 |- ( -. ch -> ps )
3		wl-mpi.2	. . 3 |- ( ph -> ( ps -> ch ) )
4	2, 3	wl-syl5 33247	. 2 |- ( ph -> ( -. ch -> ch ) )
5	4	wl-pm2.18d 33248	1 |- ( ph -> ch )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 33241  ax-luk2 33242  ax-luk3 33243

This theorem is referenced by:  wl-imim2i  33253