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;
reserve A,B for set;
reserve x,y,i,j,k for object;

theorem Th81:
  for a,b,c being object holds (a,a) --> (b,c) = a .--> c
proof
  let a,b,c be object;
  dom(a .-->c) = {a}
    .= dom({a} -->b);
  hence thesis by Th19;
end;
