Base axiom

A non-empty collection B of subsets of S is the set of bases of a matroid on S if and only if it satisfies the following condition:

• (B1) If B₁, B₂ ∈ B and x ∈ B₁\B₂, then there exists y ∈ B₂\B₁ such that (B₁ ∪ y)\x ∈ B.

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