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Metamath Proof Explorer

Theorem nfinOLD

Description: Obsolete version of nfin as of 14-May-2025. (Contributed by NM, 15-Sep-2003) (Revised by Mario Carneiro, 14-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	nfin.1	$⊢ \underline{Ⅎ} x A$
	nfin.2	$⊢ \underline{Ⅎ} x B$
Assertion	nfinOLD	$⊢ \underline{Ⅎ} x (A \cap B)$

Proof

Step	Hyp	Ref	Expression
1		nfin.1	$⊢ \underline{Ⅎ} x A$
2		nfin.2	$⊢ \underline{Ⅎ} x B$
3		dfin5	$⊢ A \cap B = \{y \in A \| y \in B\}$
4	2	nfcri	$⊢ Ⅎ x y \in B$
5	4 1	nfrabw	$⊢ \underline{Ⅎ} x \{y \in A \| y \in B\}$
6	3 5	nfcxfr	$⊢ \underline{Ⅎ} x (A \cap B)$