Theorem inton

Description: The intersection of the class of ordinal numbers is the empty set. (Contributed by NM, 20-Oct-2003)

	Ref	Expression
Assertion	inton	$$⊢\bigcap \mathrm{On}=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		0elon	$$⊢\varnothing \in \mathrm{On}$$
2		int0el	$$⊢\varnothing \in \mathrm{On}\to \bigcap \mathrm{On}=\varnothing$$
3	1 2	ax-mp	$$⊢\bigcap \mathrm{On}=\varnothing$$