Theorem ackbij1lem4

Description: Lemma for ackbij2 . (Contributed by Stefan O'Rear, 19-Nov-2014)

	Ref	Expression
Assertion	ackbij1lem4	$$⊢A\in \mathrm{\omega }\to \left\{A\right\}\in \left(𝒫\mathrm{\omega }\cap \mathrm{Fin}\right)$$

Proof

Step	Hyp	Ref	Expression
1		snelpwi	$$⊢A\in \mathrm{\omega }\to \left\{A\right\}\in 𝒫\mathrm{\omega }$$
2		snfi	$$⊢\left\{A\right\}\in \mathrm{Fin}$$
3	2	a1i	$$⊢A\in \mathrm{\omega }\to \left\{A\right\}\in \mathrm{Fin}$$
4	1 3	elind	$$⊢A\in \mathrm{\omega }\to \left\{A\right\}\in \left(𝒫\mathrm{\omega }\cap \mathrm{Fin}\right)$$