Theorem rank0

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

	Ref	Expression
Assertion	rank0	$$⊢\mathrm{rank}\left(\varnothing \right)=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢\varnothing =\varnothing$$
2		0ex	$$⊢\varnothing \in \mathrm{V}$$
3	2	rankeq0	$$⊢\varnothing =\varnothing \leftrightarrow \mathrm{rank}\left(\varnothing \right)=\varnothing$$
4	1 3	mpbi	$$⊢\mathrm{rank}\left(\varnothing \right)=\varnothing$$