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	⊢ ∅ ∈ ( 𝒫 𝐴 ∩ Fin )

Proof

Step	Hyp	Ref	Expression
1		0elpw	⊢ ∅ ∈ 𝒫 𝐴
2		0fin	⊢ ∅ ∈ Fin
3	1 2	elini	⊢ ∅ ∈ ( 𝒫 𝐴 ∩ Fin )