this post was submitted on 29 Oct 2023
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The official answer is that you cannot promote a pawn to a king, so this situation would never arise. However, this is Anarchy Chess, so let's set that aside.
If this situation did happen, and it is Black's turn, it is not checkmate, because Black's bishop takes the queen. It could not be White's turn, because there is no way to arrive at this board state on Black's turn without one or both kings being in check at the beginning of the turn, and so Black's move would have needed to remove their king from check.
Therefore, this board state is not checkmate.
The bishop is on strike as modern religious conditions makes his day-to-day services auxiliary and thus he will not attack until he gets paid
One of the kings could still pay the bishop, so still not checkmate.