Is the Friday congregational prayer obligatory when it coincides with the Eid prayer?

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The obligation of attending the Friday congregational prayer is lifted from those who have performed the Eid prayer, with the exception of the Imam. The Friday prayer does not cease to be obligatory for the Imam unless there are insufficient people present to establish the Friday prayer with him. The basis for this ruling is the tradition narrated by Iyas bin Abi Ramlah Ash-Shami, who witnessed Mu'awiyah asking Zayd bin Arqam about the Prophet's conduct when Eid and Friday coincided. Zayd confirmed that the Prophet prayed Eid and then granted leave concerning Friday, stating, "Whoever wishes to pray [Friday] may pray." Another supporting narration states, "When two Eids coincide in your day, it suffices for Friday for whoever wishes, and we shall observe the Friday prayer." Furthermore, the essence of the Friday prayer, which is the addition of the sermon, has already been fulfilled by hearing the Eid sermon, thus negating the need for a second hearing. Since their times are concurrent, one obligation is waived by the other, similar to Dhuhr with Eid.