Slate - Union is commutative

Proposition 1.1.18. Let U be a set, S, T ⊆ U. Then:

S ∪ T = T ∪ S

Proof.

Let x ∈ S ∪ T. Then x ∈ T ∪ S:
We show that x ∈ T or x ∈ S:
x ∈ S ∪ T ⇒^def x ∈ S or x ∈ T
Let x ∈ T ∪ S. Then x ∈ S ∪ T:
We show that x ∈ S or x ∈ T:
x ∈ T ∪ S ⇒^def x ∈ T or x ∈ S

References.