Theorem con3ALT2 38736

Description: Contraposition. Alternate proof of con3 149. This proof is con3ALTVD 39152 automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
con3ALT2	|- ( ( ph -> ps ) -> ( -. ps -> -. ph ) )

Proof of Theorem con3ALT2

Step	Hyp	Ref	Expression
1		notnotr 125	. . 3 |- ( -. -. ph -> ph )
2	1	imim1i 63	. 2 |- ( ( ph -> ps ) -> ( -. -. ph -> ps ) )
3	2	con1d 139	1 |- ( ( ph -> ps ) -> ( -. ps -> -. ph ) )

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)