Theorem rank0

Description: The rank of the empty set is (/) . (Contributed by Scott Fenton, 17-Jul-2015)

	Ref	Expression
Assertion	rank0	⊢ ( rank ‘ ∅ ) = ∅

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ ∅ = ∅
2		0ex	⊢ ∅ ∈ V
3	2	rankeq0	⊢ ( ∅ = ∅ ↔ ( rank ‘ ∅ ) = ∅ )
4	1 3	mpbi	⊢ ( rank ‘ ∅ ) = ∅