Let χ∈X(A) and a∈An. For every germ f∈O(Spn(a)), one has χ(Θa(f))=f(χ(a1),...,χ(an)).
This is a consequence of Proposition 3, applied to the continuous unital morphism χ:A→C (Theorem 1 of I, p. 29), and of the corollary to Proposition 2, applied to the Banach algebra C.
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.