Metamath Proof Explorer


Theorem rel0

Description: The empty set is a relation. (Contributed by NM, 26-Apr-1998)

Ref Expression
Assertion rel0 Rel ∅

Proof

Step Hyp Ref Expression
1 0ss ⊢ ∅ ⊆ ( V × V )
2 df-rel ⊢ ( Rel ∅ ↔ ∅ ⊆ ( V × V ) )
3 1 2 mpbir ⊢ Rel ∅