Theorem sseqin2

Description: A relationship between subclass and intersection. Similar to Exercise 9 of TakeutiZaring p. 18. (Contributed by NM, 17-May-1994)

	Ref	Expression
Assertion	sseqin2	$$⊢A\subseteq B\leftrightarrow B\cap A=A$$

Proof

Step	Hyp	Ref	Expression
1		dfss2	$$⊢A\subseteq B\leftrightarrow A\cap B=A$$
2		incom	$$⊢A\cap B=B\cap A$$
3	2	eqeq1i	$$⊢A\cap B=A\leftrightarrow B\cap A=A$$
4	1 3	bitri	$$⊢A\subseteq B\leftrightarrow B\cap A=A$$