
theorem Th30:
  for X,Y,x being set
  holds x in Funcs(X,Y) iff x is Function & proj1 x = X & proj2 x c= Y
proof
  let X,Y,x be set;
  hereby
    assume x in Funcs(X,Y);
    then ex f being Function st x = f & dom f = X & rng f c= Y by FUNCT_2:def 2
;
    hence x is Function & proj1 x = X & proj2 x c= Y;
  end;
  assume x is Function;
  then reconsider x as Function;
  dom x = proj1 x;
  hence thesis by FUNCT_2:def 2;
end;
