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Metamath Proof Explorer

Theorem tr0

Description: The empty set is transitive. (Contributed by NM, 16-Sep-1993)

		Ref	Expression
	Assertion	tr0	$⊢ Tr \emptyset$

Step	Hyp	Ref	Expression
1		0ss	$⊢ \emptyset \subseteq 𝒫 \emptyset$
2		dftr4	$⊢ Tr \emptyset \leftrightarrow \emptyset \subseteq 𝒫 \emptyset$
3	1 2	mpbir	$⊢ Tr \emptyset$