reserve x,y,X,Y for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,f1,f2,f3,g,g1 for PartFunc of C,COMPLEX;
reserve r1,r2,p1 for Real;
reserve r,q,cr1,cr2 for Complex;

theorem Th19:
  for f1,f2,f3 being complex-valued Function holds
  (f1 - f2)(#)f3 = f1(#)f3 - f2(#)f3
proof
  let f1,f2,f3 be complex-valued Function;
  (-f2)(#)f3 = -(f2(#)f3) by Th17;
  hence thesis by Th15;
end;
