Theorem 0finon

Description: 0 is a finite ordinal. See peano1 . (Contributed by RP, 27-Sep-2023)

	Ref	Expression
Assertion	0finon	$$⊢\varnothing \in \left(\mathrm{On}\cap \mathrm{Fin}\right)$$

Proof

Step	Hyp	Ref	Expression
1		peano1	$$⊢\varnothing \in \mathrm{\omega }$$
2		onfin2	$$⊢\mathrm{\omega }=\mathrm{On}\cap \mathrm{Fin}$$
3	1 2	eleqtri	$$⊢\varnothing \in \left(\mathrm{On}\cap \mathrm{Fin}\right)$$