Theorem ssequn2

Description: A relationship between subclass and union. (Contributed by NM, 13-Jun-1994)

	Ref	Expression
Assertion	ssequn2	$$⊢A\subseteq B\leftrightarrow B\cup A=B$$

Proof

Step	Hyp	Ref	Expression
1		ssequn1	$$⊢A\subseteq B\leftrightarrow A\cup B=B$$
2		uncom	$$⊢A\cup B=B\cup A$$
3	2	eqeq1i	$$⊢A\cup B=B\leftrightarrow B\cup A=B$$
4	1 3	bitri	$$⊢A\subseteq B\leftrightarrow B\cup A=B$$