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I've just taught this in my graduate class. Check these notes on intersection theory.
The result you want is containcontained in Thm. 4.7. Again, you need $2\dim S=\dim X$.
The result you want is contain in Thm. 4.7. Again, you need $2\dim S=\dim X$.
The result you want is contained in Thm. 4.7. Again, you need $2\dim S=\dim X$.
