Theorem ttctr3

Description: The transitive closure of a class is transitive. (Contributed by Matthew House, 6-Apr-2026)

	Ref	Expression
Assertion	ttctr3	⊢ ∪ TC+ 𝐴 ⊆ TC+ 𝐴

Proof

Step	Hyp	Ref	Expression
1		ttctr	⊢ Tr TC+ 𝐴
2		df-tr	⊢ ( Tr TC+ 𝐴 ↔ ∪ TC+ 𝐴 ⊆ TC+ 𝐴 )
3	1 2	mpbi	⊢ ∪ TC+ 𝐴 ⊆ TC+ 𝐴