Metamath Proof Explorer

Theorem nsyl

Description: A negated syllogism inference. (Contributed by NM, 31-Dec-1993) (Proof shortened by Wolf Lammen, 2-Mar-2013)

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

Proof

Step Hyp Ref Expression
1 nsyl.1 
 |-  ( ph -> -. ps )
2 nsyl.2 
 |-  ( ch -> ps )
3 1 2 nsyl3 
 |-  ( ch -> -. ph )
4 3 con2i 
 |-  ( ph -> -. ch )