reserve Y for non empty set,
  a,b,c,d for Function of Y,BOOLEAN;
reserve Y for non empty set,
  a,b,c for Function of Y,BOOLEAN;

theorem Th4:
  O_el(Y) 'nand' a = I_el(Y)
proof
  O_el(Y) 'nand' a = 'not' (O_el(Y) '&' a) & O_el(Y) '&' a = O_el(Y) by th1,
BVFUNC_1:5;
  hence thesis by BVFUNC_1:2;
end;
