
theorem
  for K be Field, K1 be Subfield of K, x, y be Element of K,
  x1, y1 be Element of K1 st x = x1 & y = y1
  holds x-y = x1-y1
  proof
    let K be Field,
    K1 be Subfield of K,
    x, y be Element of K,
    x1, y1 be Element of K1;
    set C1 = the carrier of K1;
    assume A1: x = x1 & y = y1;
    then A2: -y =-y1 by Th19;
    the addF of K1 = (the addF of K) || C1 by EC_PF_1:def 1;
    hence thesis by A1,A2,FUNCT_1:49,ZFMISC_1:87;
  end;
