בְּזֹ֖את תִּבָּחֵ֑נוּ חֵ֤י פַרְעֹה֙ אִם־תֵּצְא֣וּ מִזֶּ֔ה כִּ֧י אִם־בְּב֛וֹא אֲחִיכֶ֥ם הַקָּטֹ֖ן הֵֽנָּה׃
Hereby ye shall be proved: by the life of Pharaoh ye shall not go forth hence, except your youngest brother come hither.
Exact Source: Bereishis Rabbah 91:8
בְּזֹאת תִּבָּחֵנוּ חֵי פַרְעֹה — בְּשָׁעָה שֶׁהָיָה מְבַקֵּשׁ לִשָּׁבַע לַשֶּׁקֶר, הָיָה נִשְׁבַּע בְּחֵי פַרְעֹה.
English of Source Text: Bereishis Rabbah explains Yosef's use of “by the life of Pharaoh” as his formula when he was about to swear falsely. Rabbi Levi then gives a parable illustrating the force of Yosef's oath and his demand that the youngest brother be brought.
On the passuk: The Midrash reads Yosef's oath as part of the test he is imposing on his brothers.
Type of Learning: Derash on the verse (classic midrash) — not a formal named middah of the 13.
What Is Learned: The demand that Binyamin be brought is sealed with an oath-formula that keeps Yosef’s Egyptian persona intact while advancing the test to its next stage.