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Metamath Proof Explorer

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	$⊢ A \subseteq B$

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