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Metamath Proof Explorer

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	$⊢ A \subseteq B \leftrightarrow B \cap A = A$

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	$⊢ A \subseteq B \leftrightarrow B \cap A = A$