Theorem hash2

Description: Size of a finite ordinal. (Contributed by Mario Carneiro, 5-Jan-2016)

	Ref	Expression
Assertion	hash2	$$⊢\left|2_{𝑜}\right|=2$$

Proof

Step	Hyp	Ref	Expression
1		1onn	$$⊢1_{𝑜}\in \mathrm{\omega }$$
2		df-2o	$$⊢2_{𝑜}=\mathrm{suc}{1}_{𝑜}$$
3		hash1	$$⊢\left|1_{𝑜}\right|=1$$
4		1p1e2	$$⊢1+1=2$$
5	1 2 3 4	hashp1i	$$⊢\left|2_{𝑜}\right|=2$$