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Metamath Proof Explorer

Theorem 0pwfi

Description: The empty set is in any power set, and it's finite. (Contributed by Glauco Siliprandi, 17-Aug-2020)

		Ref	Expression
	Assertion	0pwfi	$⊢ \emptyset \in (𝒫 A \cap Fin)$

Step	Hyp	Ref	Expression
1		0elpw	$⊢ \emptyset \in 𝒫 A$
2		0fi	$⊢ \emptyset \in Fin$
3	1 2	elini	$⊢ \emptyset \in (𝒫 A \cap Fin)$