Corollary 3

Tag 03KV, permanent. Cite it as [Bourbaki, Tag 03KV].

Theory of Sets, chapter III, § 3. Equipotent sets. Cardinals

Let $\mathfrak{a}$ , $\mathfrak{b}$ , $\mathfrak{c}$ be cardinals. Then $\mathfrak{a}^{\mathfrak{b}\mathfrak{c}} = (\mathfrak{a}^{\mathfrak{b}})^{\mathfrak{c}}$ .

Let $\mathfrak{b}_\gamma = \mathfrak{b}$ for all $\gamma \in \mathfrak{c}$ . Then

\mathfrak{a}^{\mathfrak{b}\mathfrak{c}} = \mathfrak{a}^{\sum\limits_{\gamma \in \mathfrak{c}} \mathfrak{b}_\gamma} = \mathop{\mathbf{P}}_{\gamma \in \mathfrak{c}} \mathfrak{a}^{\mathfrak{b}_\gamma} = (\mathfrak{a}^{\mathfrak{b}})^{\mathfrak{c}}

by virtue of Corollary 1.

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.

Cited by

Nothing.

Cites

Corollary 1