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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 ∅

Step	Hyp	Ref	Expression
1		0ss	⊢ ∅ ⊆ 𝒫 ∅
2		dftr4	⊢ ( Tr ∅ ↔ ∅ ⊆ 𝒫 ∅ )
3	1 2	mpbir	⊢ Tr ∅