Theorem intssuni2

Description: Subclass relationship for intersection and union. (Contributed by NM, 29-Jul-2006)

	Ref	Expression
Assertion	intssuni2	$$⊢\left(A\subseteq B\wedge A\ne \varnothing \right)\to \bigcap A\subseteq \bigcup B$$

Proof

Step	Hyp	Ref	Expression
1		intssuni	$$⊢A\ne \varnothing \to \bigcap A\subseteq \bigcup A$$
2		uniss	$$⊢A\subseteq B\to \bigcup A\subseteq \bigcup B$$
3	1 2	sylan9ssr	$$⊢\left(A\subseteq B\wedge A\ne \varnothing \right)\to \bigcap A\subseteq \bigcup B$$