Metamath Proof Explorer


Theorem tr0

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

Ref Expression
Assertion tr0 Tr ∅

Proof

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