Proof 01. 1 ⊢ A ⊆ B, hypo. 02. 2 ⊢ B ⊆ C, hypo. 03. 3 ⊢ x ∈ A, hypo. 04. 1, 3 ⊢ x ∈ B, incl_elim 1 3. 05. 1, 2, 3 ⊢ x ∈ C, incl_elim 2 4. 06. 1, 2 ⊢ x ∈ A → x ∈ C, subj_intro 5. 07. 1, 2 ⊢ ∀x. x ∈ A → x ∈ C, uq_intro 6. 08. 1, 2 ⊢ A ⊆ C, incl_intro 7. incl_trans. ⊢ A ⊆ B → B ⊆ C → A ⊆ C, subj_intro_ii 8.