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
 |-  (/) C_ ~P (/)
2 dftr4
 |-  ( Tr (/) <-> (/) C_ ~P (/) )
3 1 2 mpbir
 |-  Tr (/)