Metamath Proof Explorer


Theorem ord0

Description: The empty set is an ordinal class. (Contributed by NM, 11-May-1994)

Ref Expression
Assertion ord0 Ord ∅

Proof

Step Hyp Ref Expression
1 tr0 Tr ∅
2 we0 E We ∅
3 df-ord ( Ord ∅ ↔ ( Tr ∅ ∧ E We ∅ ) )
4 1 2 3 mpbir2an Ord ∅