theorem Th17:
  not a,b // a,c & a,c // p,r & b,c // p,r implies p=r
proof
  assume that
A1: ( not a,b // a,c)& a,c // p,r and
A2: b,c // p,r;
A3: p,r // b,c by A2,Th6;
  ( not a,c // b,c)& p,r // a,c by A1,Th6,Th14;
  hence thesis by A3,Def1;
end;
