Theorem unss12

Description: Subclass law for union of classes. (Contributed by NM, 2-Jun-2004)

	Ref	Expression
Assertion	unss12	$$⊢\left(A\subseteq B\wedge C\subseteq D\right)\to A\cup C\subseteq B\cup D$$

Proof

Step	Hyp	Ref	Expression
1		unss1	$$⊢A\subseteq B\to A\cup C\subseteq B\cup C$$
2		unss2	$$⊢C\subseteq D\to B\cup C\subseteq B\cup D$$
3	1 2	sylan9ss	$$⊢\left(A\subseteq B\wedge C\subseteq D\right)\to A\cup C\subseteq B\cup D$$