Theorem ssriv

Description: Inference based on subclass definition. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypothesis	ssriv.1	$$⊢x\in A\to x\in B$$
Assertion	ssriv	$$⊢A\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		ssriv.1	$$⊢x\in A\to x\in B$$
2		df-ss	$$⊢A\subseteq B\leftrightarrow \forall x\left(x\in A\to x\in B\right)$$
3	2 1	mpgbir	$$⊢A\subseteq B$$