reserve B for non empty set,
  A,X,x for set;

theorem Th1:
  for A,B being  set, F,G being Function of A,B for X
  being set st F|X = G|X for x being Element of A st x in X holds F.x = G.x
proof
  let A,B be set, F,G be Function of A,B;
  let X be set such that
A1: F|X = G|X;
  let x be Element of A;
  assume
A2: x in X;
  hence F.x = (G|X).x by A1,FUNCT_1:49
    .= G.x by A2,FUNCT_1:49;
end;
