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Theorem con3ALT 36745
Description: Contraposition. Alternate proof of con3 139. This proof is con3ALTVD 37174 automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
con3ALT  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )

Proof of Theorem con3ALT
StepHypRef Expression
1 notnot2 115 . . 3  |-  ( -. 
-.  ph  ->  ph )
21imim1i 60 . 2  |-  ( (
ph  ->  ps )  -> 
( -.  -.  ph  ->  ps ) )
32con1d 127 1  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
Colors of variables: wff setvar class
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)
  Copyright terms: Public domain W3C validator