Theorem sssseq

Description: If a class is a subclass of another class, then the classes are equal if and only if the other class is a subclass of the first class. (Contributed by AV, 23-Dec-2020)

	Ref	Expression
Assertion	sssseq	$$⊢B\subseteq A\to \left(A\subseteq B\leftrightarrow A=B\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqss	$$⊢A=B\leftrightarrow \left(A\subseteq B\wedge B\subseteq A\right)$$
2	1	rbaibr	$$⊢B\subseteq A\to \left(A\subseteq B\leftrightarrow A=B\right)$$