Reference request: The Steenrod squares generate all stable cohomology operations

Question

The isomorphy of the Steenrod algebra to the cohomology of an Eilenberg-MacLane spectrum is a direct corollary of Brown representability and the fact, that all stable cohomology operations are generated by the Steenrod squares. However, for the latter I don't find a reference with a sound proof. May omits the proof in his Concise Course.

Thanks for the help.

Answer 1

See for example

Switzer, Robert M. Algebraic topology-homotopy and homology. Springer, 2017 (Chapter 18)

Norman Earl Steenrod, and D. B. A. Epstein. Cohomology operations. No. 50. Princeton University Press, 1962