Theorem dftr4

Description: An alternate way of defining a transitive class. Definition of Enderton p. 71. (Contributed by NM, 29-Aug-1993)

	Ref	Expression
Assertion	dftr4	$$⊢\mathrm{Tr}A\leftrightarrow A\subseteq 𝒫A$$

Proof

Step	Hyp	Ref	Expression
1		df-tr	$$⊢\mathrm{Tr}A\leftrightarrow \bigcup A\subseteq A$$
2		sspwuni	$$⊢A\subseteq 𝒫A\leftrightarrow \bigcup A\subseteq A$$
3	1 2	bitr4i	$$⊢\mathrm{Tr}A\leftrightarrow A\subseteq 𝒫A$$