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 Th51:
  a 'or' (b 'nand' c) = a 'or' 'not' b 'or' 'not' c
proof
  thus a 'or' (b 'nand' c) =a 'or' 'not' (b '&' c) by th1
    .=a 'or' ('not' b 'or' 'not' c) by BVFUNC_1:14
    .=a 'or' 'not' b 'or' 'not' c by BVFUNC_1:8;
end;
