
theorem Th1:
  for f being Function, A being set, a,b being object st a in A & b in A
  holds (f||A).(a,b) = f.(a,b)
  proof
    let f be Function;
    let A be set;
    let a,b be object;
    assume a in A & b in A;
    then [a,b] in [:A,A:] by ZFMISC_1:def 2;
    hence thesis by FUNCT_1:49;
  end;
