Theorem tr0

Description: The empty set is transitive. (Contributed by NM, 16-Sep-1993)

	Ref	Expression
Assertion	tr0	$$⊢\mathrm{Tr}\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		0ss	$$⊢\varnothing \subseteq 𝒫\varnothing$$
2		dftr4	$$⊢\mathrm{Tr}\varnothing \leftrightarrow \varnothing \subseteq 𝒫\varnothing$$
3	1 2	mpbir	$$⊢\mathrm{Tr}\varnothing$$