Theorem hash4

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

	Ref	Expression
Assertion	hash4	$$⊢\left|4_{𝑜}\right|=4$$

Proof

Step	Hyp	Ref	Expression
1		3onn	$$⊢3_{𝑜}\in \mathrm{\omega }$$
2		df-4o	$$⊢4_{𝑜}=\mathrm{suc}{3}_{𝑜}$$
3		hash3	$$⊢\left|3_{𝑜}\right|=3$$
4		3p1e4	$$⊢3+1=4$$
5	1 2 3 4	hashp1i	$$⊢\left|4_{𝑜}\right|=4$$