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 'eqv' b) = 'not' a 'or' 'not' b
proof
  thus a 'nand' (a 'eqv' b) = 'not' (a '&' (a 'eqv' b)) by th1
    .= 'not' (a '&' 'not' (a 'xor' b)) by Th12
    .= ('not' a) 'or' ('not' 'not' (a 'xor' b)) by BVFUNC_1:14
    .= ('not' a) 'or' ((a 'or' b) '&' ('not' a 'or' 'not' b))
      by BVFUNC_6:86
    .= (('not' a) 'or' (a 'or' b)) '&' (('not' a) 'or' ('not' a 'or' 'not' b
  )) by BVFUNC_1:11
    .= (('not' a) 'or' a 'or' b) '&' (('not' a) 'or' ('not' a 'or' 'not' b))
  by BVFUNC_1:8
    .= (I_el(Y) 'or' b) '&' (('not' a) 'or' ('not' a 'or' 'not' b)) by
BVFUNC_4:6
    .= I_el(Y) '&' (('not' a) 'or' ('not' a 'or' 'not' b)) by BVFUNC_1:10
    .= ('not' a) 'or' ('not' a 'or' 'not' b) by BVFUNC_1:6
    .= ('not' a) 'or' 'not' a 'or' 'not' b by BVFUNC_1:8
    .= 'not' a 'or' 'not' b;
end;
