Theorem 1n0

Description: Ordinal one is not equal to ordinal zero. (Contributed by NM, 26-Dec-2004)

	Ref	Expression
Assertion	1n0	$$⊢1_{𝑜}\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		df1o2	$$⊢1_{𝑜}=\left\{\varnothing \right\}$$
2		0ex	$$⊢\varnothing \in \mathrm{V}$$
3	2	snnz	$$⊢\left\{\varnothing \right\}\ne \varnothing$$
4	1 3	eqnetri	$$⊢1_{𝑜}\ne \varnothing$$