Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.
Wa alaikum assalam wa rahmatullahi wa barakatuh.
As to what follows:
In response to your question, we say, and with Allah Almighty lies all success:
There is no difference among the scholars that if Eid and Friday were to coincide, then it would be preferred for the one who attended the Eid Prayer to also pray the Friday Prayer. They differed, however, regarding the concession for the one who attended the Eid Prayer to not have to attend the Friday Prayer, with several opinions:
The first opinion: There is a concession for the one who performed the Eid prayer to leave off attending the Friday Prayer, and he should pray the Dhuhr Prayer instead. However, it is obligatory for the Imam to establish the Friday Prayer so that whoever wishes to perform it can do so, and also for those who did not perform the Eid Prayer. This is the opinion of the Hanbali Madh'hab.
The second opinion: There is no concession for performing the Eid Prayer and then missing the Friday Prayer upon whom it is obligatory. This is the opinion of the Hanafi Madh'hab and is also a narration of Imam Malik. This is also opined by Ibn Hazm, Ibn Mundhir and Ibn `Abdul-Barr.
The third opinion: There is a concession for country and desert folk, not city dwellers, to leave off the Friday Prayer and pray the Dhuhr Prayer instead. This is the opinion of the Shafi`i Madh'hab and is also a narration of Imam Malik.
The fourth opinion: If Eid and Friday fall on the same day, then the Eid Prayer suffices one for the reward of the Friday and Dhuhr Prayers. This is what `Ata’ bin Abi Rabbah opined, and is also reported from `Ali and Ibn Zubayr (may Allah be pleased with them).
Each group has their arguments and evidences for what they opined for, but the closest one to the truth and most pleasing evidence-wise is what Imam Ahmad opined in that there is a concession for the one who performs the Eid Prayer to leave off attending the Friday Prayer. This is evidenced by what Mu`awiyah (may Allah be pleased with him) narrated when he asked Zayd bin Arqam (may Allah be pleased with him), “Did you witness the two Eid Prayers with the Messenger of Allah (peace be upon him)?” He replied, “Yes, he performed Eid Prayer and made a concession for Friday Prayer.” [Ahmad (18831), Abu Dawud (1070), Nasa’i (1591) and others, and was authenticated by Ibn Madini and others]
They also sought evidence from the hadith narrated by Abu Hurayrah (may Allah be pleased with him) that the Prophet (peace be upon him) said, “Two Eids have coincided on this day of yours. So whoever wants, it (the Eid Prayer) will suffice him, and he will not have to pray the Friday Prayer, but we will pray the Friday Prayer.” [Abu Dawud (1073) and Ibn Majah (1311)]
This hadith is not free from criticism, but it is strengthened by the previous narration. And Allah knows best.
Dr. Khalid al-Muslih
29 / 9 / 1428 AH