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 'eqv' (a 'nor' b) = 'not' a '&' b
proof
  thus a 'eqv' (a 'nor' b) =(a 'or' a 'or' b) '&' ('not' a 'or' 'not' (a 'or'
  b)) by Th64
    .=((a 'or' b) '&' 'not' a) 'or' ((a 'or' b) '&' 'not' (a 'or' b)) by
BVFUNC_1:12
    .=((a 'or' b) '&' 'not' a) 'or' O_el(Y) by BVFUNC_4:5
    .=(a 'or' b) '&' 'not' a by BVFUNC_1:9
    .=(a '&' 'not' a) 'or' (b '&' 'not' a) by BVFUNC_1:12
    .=O_el(Y) 'or' (b '&' 'not' a) by BVFUNC_4:5
    .='not' a '&' b by BVFUNC_1:9;
end;
