This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem nsyl2

Description: A negated syllogism inference. (Contributed by NM, 26-Jun-1994) (Proof shortened by Wolf Lammen, 14-Nov-2023)

Ref Expression
Hypotheses nsyl2.1 
|- ( ph -> -. ps )
nsyl2.2 
|- ( -. ch -> ps )
Assertion nsyl2 
|- ( ph -> ch )

Proof

Step Hyp Ref Expression
1 nsyl2.1 
 |-  ( ph -> -. ps )
2 nsyl2.2 
 |-  ( -. ch -> ps )
3 1 2 nsyl3 
 |-  ( -. ch -> -. ph )
4 3 con4i 
 |-  ( ph -> ch )