In Ya'aleh V'yavo, in tefilla for the 3 regalim and in Kiddush for the regalim, we have options for the particular Yom Tov. The specific day is listed, and is always introduced with the word "b'yom" (on the day).
לְחֵן וּלְחֶסֶד וּלְרַחֲמִים. לְחַיִּים וּלְשָׁלום בְּיום:
בראש חדש - ראשׁ הַחדֶשׁ:
בפסח - חַג הַמַּצּות:
בסוכות - חַג הַסֻּכּות:
Why does the formulation codify the "b'yom"? If the phrase was "ul'shalom b'rosh hachodesh", or "ul'sason b'chag hamatzot..." would it lose anything in terms of meaning? Is the double language of calling it a day and a chag necessary?