“Question: On the first day of Pesach the ba’al koreh only leined Maftir from v’hikravtem [as opposed to u’vachodesh horishon]. Is this acceptable b’dieved?
Discussion: The Shulchan Aruch (Orach Chayim Siman 137 se’if 3) discusses a situation where a ba’al koreh omitted a possuk from keriyas hatorah, and writes that each and every possuk is essential on Shabbos [morning], and if the ba’al koreh omitted a possuk then one needs to go back and lein the possuk that was omitted, even if [the mistake was only realised] after the sefer torah has already been returned. The Shulchan Aruch (ibid) tells us that in this situation, the Sefer Torah must be taken out again, and the omitted possuk leined (together with another two pesukim, because we do not lein less than three pesukim together).
However, if the omission occurred on a Monday, Thurday or during Mincha on Shabbos, then if the minimum ten obligatory pesukim have been leined one does not need to go back and read the omitted possuk.
Regarding keriyas hatorah on Yom Tov, the Shulchan Aruch (ibid) writes that [an omission during keriyas hatorah on] Yom Tov has the same din as [an omission during keriyas hatorah on] on Monday, Thurday or during Mincha on Shabbos [and there is no need to repeat if a posuk was omitted]. The Mishna Berura (ibid s.k. 11) points out that this is specifically if five aliyos were leined, and each aliya contains at least three pesukim. (In Bi’ur Halocho d.h. “parshiyos” the Mishna Berura discusses what the din should be if the omission pertains to the current Yom Tov.)
Regarding maftir, the Magen Avraham (ibid, s.k. 6) discusses at length if one needs to go back if one forgot to lein maftir and concludes that if a tzibbur forgot to lein maftir then they do need to go back and lein maftir. However, if a single posuk was omitted then one does not need to go back and lein maftir again. The Magen Avraham does not differentiate between whether the omitted possuk was a vital component of the maftir or not (a vital component would be any of the korbonos hayom).
The Mishna Berura (ibid quoting the Elya Rabbah) writes that if the omitted posuk was a vital component of the maftir then maftir does need to be repeated. One of the examples brought by the Mishna Berura of a vital component of the maftir is if the ba’al koreh omitted on the first day of Pesach a posuk from “v’hikravtem” until the end of the korbonos listed. It is clear from context that the pesukim preceding “v’hikravtem” are considered non-essential pesukim that do not require repeating maftir [because they do not denote any of the korbonos hayom].
This is also clearly written in Sha’arei Efrayim (Sha’ar 8 se’if 3); that if the ba’al koreh began maftir on the first day of Pesach from “v’hikravtem” then one does not need to repeat maftir. (However, if the oleh has not yet said the second brocho then the ba’al koreh should repeat the keriya of maftir correctly.)
Conclusion: If on the first day of Pesach the ba’al koreh began Maftir from “v’hikravtem” and the mistake was only realised after the oleh had recited the brochos after his aliya, the keriya is valid and does not need to be repeated. This is because the pesukim preceding “v’hikravtem” do not denote the korbonos and therefore are not considered an essential component of the maftir. However, if the mistake was realised before the oleh recited the final brocho after his aliya, then the ba’al koreh should go back and lein maftir correctly.
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