
theorem Th5:
  for X,Y being non empty set, y being Element of Y holds
  [:X,{y}:] c= union Funcs(X,Y)
  proof
    let X,Y be non empty set;
    let y be Element of Y;
    let o be object;
    assume o in [:X,{y}:];
    then o in X --> y in Funcs(X,Y) by FUNCT_2:8;
    hence o in union Funcs(X,Y) by TARSKI:def 4;
  end;
