Theorem 1finon

Description: 1 is a finite ordinal. See 1onn . (Contributed by RP, 27-Sep-2023)

	Ref	Expression
Assertion	1finon	$$⊢1_{𝑜}\in \left(\mathrm{On}\cap \mathrm{Fin}\right)$$

Proof

Step	Hyp	Ref	Expression
1		1onn	$$⊢1_{𝑜}\in \mathrm{\omega }$$
2		onfin2	$$⊢\mathrm{\omega }=\mathrm{On}\cap \mathrm{Fin}$$
3	1 2	eleqtri	$$⊢1_{𝑜}\in \left(\mathrm{On}\cap \mathrm{Fin}\right)$$