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Why is Kc3 illegal in this position?

<Comment deleted by user>
Because Black will take your king before you take theirs, and obviously taking a king is illegal. Even if the knight is pinned to the king, it still serves control of that square to not allow the White king to move there.
FIDE says:

3.9 The king is said to be 'in check' if it is attacked by one or more of the opponent's pieces,
even if such pieces are constrained from moving to that square because they would then
leave or place their own king in check. No piece can be moved that will either expose the
king of the same colour to check or leave that king in check.
Thanks for the quote!

@Sarg0n said in #5:
> FIDE says:
>
> 3.9 The king is said to be 'in check' if it is attacked by one or more of the opponent's pieces,
> even if such pieces are constrained from moving to that square because they would then
> leave or place their own king in check. No piece can be moved that will either expose the
> king of the same colour to check or leave that king in check.
Because even though Black's knight is perfectly immobilized - given the absolute pin to Black's King the knight is in, without ability to take the attacking Bishop piece, or move along that diagonal inbetween; Black's knight still has influence on the c3 square; therefore White's King can't move to a square it has influence on - that would be White walking the King into check.
And besides, the trade of kings isn't supposed to be something that should be considered in chess, because once a King is first lost; the chess game would be over.
@Sarg0n said in #5:
> FIDE says:
>
> 3.9 The king is said to be 'in check' if it is attacked by one or more of the opponent's pieces,
> even if such pieces are constrained from moving to that square because they would then
> leave or place their own king in check. No piece can be moved that will either expose the
> king of the same colour to check or leave that king in check.

Yes, but I have made the rule better.
Remember when I suggested changes in rules of chess.
One was about that absolute pinned pieces should not be able to control the pieces.
And I had proper response for your words there.
See: lichess.org/forum/general-chess-discussion/my-opinion-two-chess-rules-should-be-revised#1

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