rw [← indep_singleton, uniqueBaseOn_indep_iff', singleton_subset_iff]
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I✝ X Y Z F C K I E : Set α
⊢ (uniqueBaseOn I E).Nonloop e ↔ e ∈ I ∩ E
no goals