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 'nor' b) = a 'or' 'not' b
proof
  thus a 'xor' (a 'nor' b) =(a 'or' 'not' (a 'or' b)) '&' ('not' a 'or' a 'or'
  b) by Th63
    .=(a 'or' 'not' (a 'or' b)) '&' (I_el(Y) 'or' b) by BVFUNC_4:6
    .=(a 'or' 'not' (a 'or' b)) '&' I_el(Y) by BVFUNC_1:10
    .=a 'or' 'not' (a 'or' b) by BVFUNC_1:6
    .=a 'or' ('not' a '&' 'not' b) by BVFUNC_1:13
    .=(a 'or' 'not' a) '&' (a 'or' 'not' b) by BVFUNC_1:11
    .=I_el(Y) '&' (a 'or' 'not' b) by BVFUNC_4:6
    .=a 'or' 'not' b by BVFUNC_1:6;
end;
