Thus the doubts of Vasudeva were dispelled - by hearing the words of Nanda Maharaja in SB 10.5.29

Expressions researched:
"Thus the doubts of Vasudeva were dispelled"

Srimad-Bhagavatam

SB Canto 10.1 to 10.13

When Vasudeva understood from Nanda Mahārāja that the mystery of Kṛṣṇa's birth and His having been exchanged with Yaśodā's daughter was yet undisclosed, he was happy that things were going on nicely. By saying that Vasudeva's daughter, his youngest child, had gone to the heavenly planets, Nanda Mahārāja indicated that he did not know that this daughter was born of Yaśodā and that Vasudeva had exchanged her with Kṛṣṇa. Thus the doubts of Vasudeva were dispelled.

SB 10.5.29, Translation and Purport

Nanda Mahārāja said: Alas, King Kaṁsa killed so many of your children, born of Devakī. And your one daughter, the youngest child of all, entered the heavenly planets.

When Vasudeva understood from Nanda Mahārāja that the mystery of Kṛṣṇa's birth and His having been exchanged with Yaśodā's daughter was yet undisclosed, he was happy that things were going on nicely. By saying that Vasudeva's daughter, his youngest child, had gone to the heavenly planets, Nanda Mahārāja indicated that he did not know that this daughter was born of Yaśodā and that Vasudeva had exchanged her with Kṛṣṇa. Thus the doubts of Vasudeva were dispelled.