Theorem hash3

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

	Ref	Expression
Assertion	hash3	$$⊢\left|3_{𝑜}\right|=3$$

Proof

Step	Hyp	Ref	Expression
1		2onn	$$⊢2_{𝑜}\in \mathrm{\omega }$$
2		df-3o	$$⊢3_{𝑜}=\mathrm{suc}{2}_{𝑜}$$
3		hash2	$$⊢\left|2_{𝑜}\right|=2$$
4		2p1e3	$$⊢2+1=3$$
5	1 2 3 4	hashp1i	$$⊢\left|3_{𝑜}\right|=3$$