Reconfirming The Next Successor

I Kings 1:28-31

28  Then king David answered and said, Call me Bathsheba. And she came into the king's presence, and stood before the king. 
29  And the king sware, and said, As the LORD liveth, that hath redeemed my soul out of all distress, 
30  Even as I sware unto thee by the LORD God of Israel, saying, Assuredly Solomon thy son shall reign after me, and he shall sit upon my throne in my stead; even so will I certainly do this day. 
31  Then Bathsheba bowed with her face to the earth, and did reverence to the king, and said, Let my lord king David live for ever.