I know that two sets are equinumerous if there exist a bijection between them, and they are uncountables if there exist another bijection between the real numbers from 0 to 1 and a set.
So, as they requiere both conditions, can I maintain that they are equinumerous?
No you cannot prove this statement because it is false. Cantor showed that the power set of a set is strictly larger than the set. The reals are uncountable and the power set of the reals is strictly larger, so these two sets are not equinumerous. In fact there is a huge number of uncountable cardinalities.