Theorem pm2.21ddALT 119

Description: Alternate proof of pm2.21dd 186. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
pm2.21ddALT.1	|- ( ph -> ps )
pm2.21ddALT.2	|- ( ph -> -. ps )

Assertion

Ref	Expression
pm2.21ddALT	|- ( ph -> ch )

Proof of Theorem pm2.21ddALT

Step	Hyp	Ref	Expression
1		pm2.21ddALT.1	. 2 |- ( ph -> ps )
2		pm2.21ddALT.2	. . 3 |- ( ph -> -. ps )
3	2	pm2.21d 118	. 2 |- ( ph -> ( ps -> ch ) )
4	1, 3	mpd 15	1 |- ( ph -> ch )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by: (None)