What happens if a king check a king?

What happens if a king check a king? A king cannot itself directly check the opposing king, since this would place the first king in check as well. A move of the king could expose the opposing king to a discovered check by another piece, however.

A king cannot itself directly check the opposing king, since this would place the first king in check as well. A move of the king could expose the opposing king to a discovered check by another piece, however.