reserve c,c1,c2,x,y,z,z1,z2 for set;
reserve C1,C2,C3 for non empty set;

theorem
  for X,Y being non empty set for x being Element of X, y being Element
of Y holds (x = y implies Imf(X,Y).(x,y) = 1) & (x <> y implies Imf(X,Y).(x,y)
  = 0)
proof
  let X,Y being non empty set;
  let x being Element of X, y being Element of Y;
  [x,y] in [:X,Y:] by ZFMISC_1:87;
  hence thesis by Def4;
end;
