reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

theorem
  for a,b,x,y,x9,y9 being object st a <> b & (a,b) --> (x,y) = (a,b) --> (
  x9,y9) holds x = x9 & y = y9
proof
  let a,b,x,y,x9,y9 be object such that
A1: a <> b and
A2: (a,b) --> (x,y) = (a,b) --> (x9,y9);
  thus x = ((a,b) --> (x,y)).a by A1,Th63
    .= x9 by A1,A2,Th63;
  thus y = ((a,b) --> (x,y)).b by Th63
    .= y9 by A2,Th63;
end;
