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Metamath Proof Explorer

Theorem ssinss1

Description: Intersection preserves subclass relationship. (Contributed by NM, 14-Sep-1999)

		Ref	Expression
	Assertion	ssinss1	$⊢ A \subseteq C \to A \cap B \subseteq C$

Step	Hyp	Ref	Expression
1		inss1	$⊢ A \cap B \subseteq A$
2		sstr2	$⊢ A \cap B \subseteq A \to (A \subseteq C \to A \cap B \subseteq C)$
3	1 2	ax-mp	$⊢ A \subseteq C \to A \cap B \subseteq C$