Metamath Proof Explorer

Theorem mtoi

Description: Modus tollens inference. (Contributed by NM, 5-Jul-1994) (Proof shortened by Wolf Lammen, 15-Sep-2012)

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

Proof

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