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 'or' (a 'nand' b) = I_el(Y)
proof
  thus a 'or' (a 'nand' b) =a 'or' 'not' a 'or' 'not' b by Th51
    .=I_el(Y) 'or' 'not' b by BVFUNC_4:6
    .=I_el(Y) by BVFUNC_1:10;
end;
