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Metamath Proof Explorer

Theorem dfin5

Description: Alternate definition for the intersection of two classes. (Contributed by NM, 6-Jul-2005)

		Ref	Expression
	Assertion	dfin5	$⊢ A \cap B = \{x \in A \| x \in B\}$

Step	Hyp	Ref	Expression
1		df-in	$⊢ A \cap B = \{x \| (x \in A \land x \in B)\}$
2		df-rab	$⊢ \{x \in A \| x \in B\} = \{x \| (x \in A \land x \in B)\}$
3	1 2	eqtr4i	$⊢ A \cap B = \{x \in A \| x \in B\}$