theorem
  a,b // a,x & b,c // b,x & c,a // c,x implies a,b // a,c
proof
  assume that
A1: a,b // a,x and
A2: b,c // b,x and
A3: c,a // c,x;
  now
    assume
A4: a<>x;
    a,x // a,b & a,x // a,c by A1,A3,Th7;
    hence thesis by A4,Def1;
  end;
  hence thesis by A2,Th7;
end;
