Halakhah for Shevuot 70:27

התם שבועת האלה כתיב הכי קאמר אלה אין אלה אלא בשבועה וכן הוא אומר והשביע הכהן את האשה בשבועת האלה

and if they did not receive on tradition this Gezerah shawah, how do they know that 'alah'<span class="x" onmousemove="('comment',' Mentioned in Lev. V. 1.');">⁵²</span> implies an oath?<span class="x" onmousemove="('comment',' For in the case of adjuration, oath is not mentioned in the verse.');">⁵³</span> - They deduce it front [the Baraitha in] which it was taught.' Alah':<span class="x" onmousemove="('comment',' Mentioned in Lev. V. 1.');">⁵²</span> 'alah' is nothing but the expression of an oath; and so it says: And the priest shall cause the woman to swear with the oath of alah.<span class="x" onmousemove="('comment',' Num. V, 21. This proves that 'alah' implies an oath.');">⁵⁴</span> But there it is written: the oath of alah!<span class="x" onmousemove="('comment',' [This is a new question: the phrase 'the oath of alah' indeed proves that 'alah' implies an oath, but whence do we know that an oath without an accompanying 'alah' (curse) is an oath? V. n. 7.]');">⁵⁵</span> - Thus he means: 'alah'; 'alah' can only be an oath,<span class="x" onmousemove="('comment',' [So MS.M. V. Sifra on Lev. V, 1; cur. edd.: with an oath; cf. n. 7.]');">⁵⁶</span> and thus it says: 'and the priest shall cause the woman to swear with the oath of alah.'

Sefer HaChinukh