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Metamath Proof Explorer

Theorem bnj1322

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

		Ref	Expression
	Assertion	bnj1322	$⊢ A = B \to A \cap B = A$

Step	Hyp	Ref	Expression
1		eqimss	$⊢ A = B \to A \subseteq B$
2		dfss2	$⊢ A \subseteq B \leftrightarrow A \cap B = A$
3	1 2	sylib	$⊢ A = B \to A \cap B = A$