simp only [Set.mem_setOf_eq, and_imp] at h ⊢
α : Type u_1
I✝ : Set α
M : Matroid α
I X J : Set α
hX : X ⊆ M.E
h :
  J ∈
    {a |
      a ∈ {I' | M.Indep I' ∧ I ⊆ I' ∧ I' ⊆ X} ∧
        ∀ ⦃b : Set α⦄,
          b ∈ {I' | M.Indep I' ∧ I ⊆ I' ∧ I' ⊆ X} → (fun x x_1 => x ⊆ x_1) a b → (fun x x_1 => x ⊆ x_1) b a}
⊢ J ∈
      {a |
        a ∈ {A | M.Indep A ∧ A ⊆ X} ∧
          ∀ ⦃b : Set α⦄, b ∈ {A | M.Indep A ∧ A ⊆ X} → (fun x x_1 => x ⊆ x_1) a b → (fun x x_1 => x ⊆ x_1) b a} ∧
    X ⊆ M.E
α : Type u_1
I✝ : Set α
M : Matroid α
I X J : Set α
hX : X ⊆ M.E
h : (M.Indep J ∧ I ⊆ J ∧ J ⊆ X) ∧ ∀ ⦃b : Set α⦄, M.Indep b → I ⊆ b → b ⊆ X → J ⊆ b → b ⊆ J
⊢ ((M.Indep J ∧ J ⊆ X) ∧ ∀ ⦃b : Set α⦄, M.Indep b → b ⊆ X → J ⊆ b → b ⊆ J) ∧ X ⊆ M.E