Theorem union_incl_right

Theorem. union_incl_right
B ⊆ A ∪ B
Proof
01. 1 ⊢ x ∈ B, hypo.
02. 1 ⊢ x ∈ A ∪ B, union_intror 1.
03. ⊢ x ∈ B → x ∈ A ∪ B, subj_intro 2.
04. ⊢ ∀x. x ∈ B → x ∈ A ∪ B, uq_intro 3.
union_incl_right. ⊢ B ⊆ A ∪ B, incl_intro 4.

Dependencies
The given proof depends on three axioms:
comp, eq_refl, eq_subst.