Hopf invariant and the linking number

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The Hopf invariant of a map $f:S^{2n-1}\to S^n$ can be defined in various ways, in particular:

(1) as the linking number of the preimages of two points and

(2) using the cohomology ring of the space $S^n\cup_f D^{2n}$.

Where can I find a proof of equivalence of these two definitions?

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Historical reference is

Steenrod N. E. Cohomology invariants of mappings // Ann. Math. 1949. V. 50. P. 954—988.