1 Kings 1:17
And she said unto him, My lord, thou swarest by the LORD thy God unto thine handmaid, saying, Assuredly Solomon thy son shall reign after me, and he shall sit upon my throne. And she said unto him, My lord, thou swarest by the LORD thy God unto thine handmaid, saying, Assuredly Solomon thy son shall reign after me, and he shall sit upon my throne.
Bathsheba's words recall David's sworn oath to her that her son Solomon would reign after him and sit upon his throne. That oath made Solomon's succession a settled promise, not a later arrangement. It also expressed God's own direction for who should succeed David.
When Adonijah moved to seize the throne, Bathsheba with others brought that promise back before David, urging him to act on the divine direction it contained. David in response reaffirmed the oath and confirmed Solomon as his successor. He then stepped aside from rule in Solomon's favor, abdicating to make way for him. Solomon was thereupon anointed and publicly proclaimed king, so that the oath was fulfilled in his accession.