Axiom:Marriage Condition

Definition
Let $\SS = \family {S_k}_{k \mathop \in I}$ be an indexed family of finite sets.

For each $F \subseteq I$, let:
 * $\ds Y_F = \bigcup_{k \mathop \in F} S_k$.

$\SS$ satisfies the marriage condition :
 * for each finite subset $F \subseteq I : \card F \le \card {Y_F}$.