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Metamath Proof Explorer

Theorem rabfi

Description: A restricted class built from a finite set is finite. (Contributed by Thierry Arnoux, 14-Feb-2017)

		Ref	Expression
	Assertion	rabfi	$⊢ A \in Fin \to \{x \in A \| φ\} \in Fin$

Step	Hyp	Ref	Expression
1		dfrab3	$⊢ \{x \in A \| φ\} = A \cap \{x \| φ\}$
2		infi	$⊢ A \in Fin \to A \cap \{x \| φ\} \in Fin$
3	1 2	eqeltrid	$⊢ A \in Fin \to \{x \in A \| φ\} \in Fin$