A W-Wing uses two far-apart cells that both contain only XY, joined by a strong link on X (or on Y) somewhere between them.
Before this: Comfort with bi-value cells and strong links helps.
Why it works
Suppose the bridge is a strong link on X. Then one end of that bridge is X, which forces one of the XY cells away from X — so that XY cell becomes Y. Careful chaining shows that at least one of the two XY cells must be Y.
Therefore any cell that sees both XY cells cannot be Y.
(The mirror argument works if the strong link is on Y instead.)
Demonstration
Find two cells that both contain only XY. They look identical — but they may be far apart.
Connect their neighborhoods with a strong conjugate link on one of those digits. The green cells form a W-Wing. The digit we can attack is 5.
The strong link forces at least one of the XY cells to be 5 — both bridge worlds leave that digit true at an end.
Eliminate 5 from cells that see both XY cells (red).
Example 1
Find two identical bi-value cells linked by a strong conjugate.
This W-Wing eliminates 5.
Remove 5 from cells that see both ends (red). At least one XY cell must be that digit.
Example 2
Find two identical bi-value cells linked by a strong conjugate.
This W-Wing eliminates 2.
Remove 2 from cells that see both ends (red). At least one XY cell must be that digit.