theorem
  for G,H being strict Group holds Ker 1:(G,H) = G
proof
  let G,H be strict Group;
  now
    let a be Element of G;
    1:(G,H).a = 1_H;
    hence a in Ker 1:(G,H) by Th41;
  end;
  hence thesis by GROUP_2:62;
end;
