at is substituted for the Ablative -5th case ending bhyas after the aṅga (stems) yuṣmad and asmad,
As युष्मत्, अस्मत् ॥ The द् is elided by 7.2.95, before the case ending भ्यस्, and युष्म + अत् = युष्मत् by (VI. I. 97).,
पञ्चम्या अत्
Adhyāya 7 · Pāda 1 · Rule 31