Theorem ssun1

Description: Subclass relationship for union of classes. Theorem 25 of Suppes p. 27. (Contributed by NM, 5-Aug-1993)

	Ref	Expression
Assertion	ssun1	$$⊢A\subseteq A\cup B$$

Proof

Step	Hyp	Ref	Expression
1		orc	$$⊢x\in A\to \left(x\in A\vee x\in B\right)$$
2		elun	$$⊢x\in \left(A\cup B\right)\leftrightarrow \left(x\in A\vee x\in B\right)$$
3	1 2	sylibr	$$⊢x\in A\to x\in \left(A\cup B\right)$$
4	3	ssriv	$$⊢A\subseteq A\cup B$$