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
  a 'nand' (a 'nor' b) = I_el(Y)
proof
  thus a 'nand' (a 'nor' b) = 'not' (a '&' (a 'nor' b)) by th1
    .= 'not' (a '&' 'not' (a 'or' b)) by Th2
    .= ('not' a) 'or' ('not' 'not' (a 'or' b)) by BVFUNC_1:14
    .= ('not' a) 'or' a 'or' b by BVFUNC_1:8
    .= I_el(Y) 'or' b by BVFUNC_4:6
    .= I_el(Y) by BVFUNC_1:10;
end;
