theorem Th32:
  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,Th23;
  ( not a,c '||' b,c)& p,r '||' a,c by A1,Th23,Th29;
  hence thesis by A3,Def11;
end;
