Theorem trv

Description: The universe is transitive. (Contributed by NM, 14-Sep-2003)

	Ref	Expression
Assertion	trv	$$⊢\mathrm{Tr}\mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		ssv	$$⊢\bigcup \mathrm{V}\subseteq \mathrm{V}$$
2		df-tr	$$⊢\mathrm{Tr}\mathrm{V}\leftrightarrow \bigcup \mathrm{V}\subseteq \mathrm{V}$$
3	1 2	mpbir	$$⊢\mathrm{Tr}\mathrm{V}$$