וַיְבִאֶהָ יִצְחָק הָאֹהֱלָה שָׂרָה אִמּוֹ וַיִּקַּח אֶת־רִבְקָה וַתְּהִי־לוֹ לְאִשָּׁה
וַיֶּאֱהָבֶהָ וַיִּנָּחֵם יִצְחָק אַחֲרֵי אִמּוֹ׃
Isaac then brought her into the tent of his mother Sarah, and he took Rebekah as his wife. Isaac loved her, and thus found comfort after his mother’s death. (Gen 24.67)
As we know from Hilchos Kiddushin - bringing the bride home substitutes Nissuin (closeness, also from ביאה) and "taking as a wife" is only Kiddushin.
So it looks that either Itzhak reversed the Halachic order or was he marrying BY Nissuin (which is Rabbinically prohibited.
I thought about Eliezer's actions that some say constituted Kiddushin, but then the verse is still in reverse order.
How the verse can be explained?