When can ZFC be said to have been "born"? The "History" section of the Wikipedia article on ZFC isn't particularly helpful. The only thing I have understood from it is that ZFC had appeared after 1922. In what book or paper was ZFC first explicitly formulated and proposed?

Here are some relevant quotes from Fraenkel, Bar-Hillel, Levy's  "Foundations of set theory":
"Zermelo's vague notion of a definite statement did not live up to the standard of rigor customary in mathematics ... In 1921/22, independently and almost simultaneously, two different methods were offered [by Fraenkel and Skolem] for replacing in the axiom of subsets the vague notion of a definite statement by a well-defined, and therefore much more restricted, notion of a statement ... The second method, proposed by Skolem and, by now, universally accepted because of its universality and generality ... It [The axiom schema of replacement] was suggested first by Fraenkel and independently by Skolem."
An english translation of Skolem's "Some remarks on axiomatized set theory" appears in Heijenoort's "From Frege to Godel - A source book in mathematical logic". The commentary on Skolem's paper says (and I agree): 
"These indications do not exhaust the content of a rich and clearly written paper, which when it was published did not receive the attention it deserved, although it heralded important future developments".
