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 ↔ ∪ 𝐴 ⊆ 𝐴 )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	⊢ 𝐴
1	0	wtr	⊢ Tr 𝐴
2	0	cuni	⊢ ∪ 𝐴
3	2 0	wss	⊢ ∪ 𝐴 ⊆ 𝐴
4	1 3	wb	⊢ ( Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴 )