Metamath Proof Explorer

Theorem mt3i

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

Ref Expression
Hypotheses mt3i.1 
|- -. ch
mt3i.2 
|- ( ph -> ( -. ps -> ch ) )
Assertion mt3i 
|- ( ph -> ps )

Proof

Step Hyp Ref Expression
1 mt3i.1 
 |-  -. ch
2 mt3i.2 
 |-  ( ph -> ( -. ps -> ch ) )
3 1 a1i 
 |-  ( ph -> -. ch )
4 3 2 mt3d 
 |-  ( ph -> ps )