Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  con3ALT Unicode version

Theorem con3ALT 28293
Description: Contraposition. Alternate proof of con3 126. This proof is con3ALTVD 28692 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 104 . . 3  |-  ( -. 
-.  ph  ->  ph )
21imim1i 54 . 2  |-  ( (
ph  ->  ps )  -> 
( -.  -.  ph  ->  ps ) )
32con1d 116 1  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
  Copyright terms: Public domain W3C validator