Metamath Proof Explorer


Definition df-tr

Description: Define the transitive class predicate. Not to be confused with a transitive relation (see cotr ). Definition of Enderton p. 71 extended to arbitrary classes. For alternate definitions, see dftr2 (which is suggestive of the word "transitive"), dftr3 , dftr4 , dftr5 , and (when A is a set) unisuc . The term "complete" is used instead of "transitive" in Definition 3 of Suppes p. 130. (Contributed by NM, 29-Aug-1993)

Ref Expression
Assertion df-tr ( Tr 𝐴 𝐴𝐴 )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA 𝐴
1 0 wtr Tr 𝐴
2 0 cuni 𝐴
3 2 0 wss 𝐴𝐴
4 1 3 wb ( Tr 𝐴 𝐴𝐴 )