What is the ruling on a secret second marriage, its denial, and swearing an oath that it did not occur?

The first wife does not have the right to prevent her husband from marrying another woman or to reject it, as it is permissible for him if he is able to provide for and deal justly with them. If a man marries a second wife with a valid marriage that fulfills all conditions and pillars, then it is a sound marriage. The husband's denial of his marriage to her and his swearing to his first wife that he did not marry does not invalidate the marriage, nor is it considered an explicit divorce for the second wife. Rather, it is an implicit statement (kinayah) that could mean divorce or something else. If by his denial he intended to lie or that he did not have a woman who pleased him, then no divorce occurs. However, if he intended divorce by his denial, then it occurs.