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 'xor' (a 'nand' b) = 'not' a 'or' b
proof
  thus a 'xor' (a 'nand' b) =('not' a '&' 'not' (a '&' b)) 'or' (a '&' a '&' b
  ) by Th52
    .=('not' a 'or' (a '&' b)) '&' ('not' (a '&' b) 'or' (a '&' b)) by
BVFUNC_1:11
    .=('not' a 'or' (a '&' b)) '&' I_el(Y) by BVFUNC_4:6
    .='not' a 'or' (a '&' b) by BVFUNC_1:6
    .=('not' a 'or' a) '&' ('not' a 'or' b) by BVFUNC_1:11
    .=I_el(Y) '&' ('not' a 'or' b) by BVFUNC_4:6
    .='not' a 'or' b by BVFUNC_1:6;
end;
