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My pawn is pinned by the enemy bishop, however if I push the pinned pawn 1 space my rook would then put the opposing king in check resulting in a simultaneous check with my opponent to move next Can I move my pinned pawn in that situation?

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No. Doing so would put you in check, and it would be the enemy's turn.

You can think of it this way, the enemy would have the first opportunity to take a king, so if the game was about taking kings, then you would lose in this situation.

You can never make a move that would allow the enemy to take your king, even if you put their king in check at the same time.

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