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Metamath Proof Explorer

Theorem dfss

Description: Variant of subclass definition dfss2 . (Contributed by NM, 21-Jun-1993)

		Ref	Expression
	Assertion	dfss	$⊢ A \subseteq B \leftrightarrow A = A \cap B$

Step	Hyp	Ref	Expression
1		dfss2	$⊢ A \subseteq B \leftrightarrow A \cap B = A$
2		eqcom	$⊢ A \cap B = A \leftrightarrow A = A \cap B$
3	1 2	bitri	$⊢ A \subseteq B \leftrightarrow A = A \cap B$