Metamath Proof Explorer

Theorem mt2i

Description: Modus tollens inference. (Contributed by NM, 26-Mar-1995) (Proof shortened by Wolf Lammen, 15-Sep-2012)

Ref Expression
Hypotheses mt2i.1 
|- ch
mt2i.2 
|- ( ph -> ( ps -> -. ch ) )
Assertion mt2i 
|- ( ph -> -. ps )

Proof

Step Hyp Ref Expression
1 mt2i.1 
 |-  ch
2 mt2i.2 
 |-  ( ph -> ( ps -> -. ch ) )
3 1 a1i 
 |-  ( ph -> ch )
4 3 2 mt2d 
 |-  ( ph -> -. ps )