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	⊢ ∩ On = ∅

Proof

Step	Hyp	Ref	Expression
1		0elon	⊢ ∅ ∈ On
2		int0el	⊢ ( ∅ ∈ On → ∩ On = ∅ )
3	1 2	ax-mp	⊢ ∩ On = ∅