Theorem intv

Description: The intersection of the universal class is empty. (Contributed by NM, 11-Sep-2008)

	Ref	Expression
Assertion	intv	$$⊢\bigcap \mathrm{V}=\varnothing$$

Proof

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