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Metamath Proof Explorer

Theorem trv

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

		Ref	Expression
	Assertion	trv	$⊢ Tr V$

Step	Hyp	Ref	Expression
1		ssv	$⊢ ⋃ V \subseteq V$
2		df-tr	$⊢ Tr V \leftrightarrow ⋃ V \subseteq V$
3	1 2	mpbir	$⊢ Tr V$