Theorem ssun

Description: A condition that implies inclusion in the union of two classes. (Contributed by NM, 23-Nov-2003)

	Ref	Expression
Assertion	ssun	$$⊢\left(A\subseteq B\vee A\subseteq C\right)\to A\subseteq B\cup C$$

Proof

Step	Hyp	Ref	Expression
1		ssun3	$$⊢A\subseteq B\to A\subseteq B\cup C$$
2		ssun4	$$⊢A\subseteq C\to A\subseteq B\cup C$$
3	1 2	jaoi	$$⊢\left(A\subseteq B\vee A\subseteq C\right)\to A\subseteq B\cup C$$