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	$$⊢\varnothing \in \left(𝒫A\cap \mathrm{Fin}\right)$$

Proof

Step	Hyp	Ref	Expression
1		0elpw	$$⊢\varnothing \in 𝒫A$$
2		0fin	$$⊢\varnothing \in \mathrm{Fin}$$
3	1 2	elini	$$⊢\varnothing \in \left(𝒫A\cap \mathrm{Fin}\right)$$