Theorem ttcidm

Description: The transitive closure operation is idempotent. (Contributed by Matthew House, 6-Apr-2026)

	Ref	Expression
Assertion	ttcidm	⊢ TC+ TC+ 𝐴 = TC+ 𝐴

Proof

Step	Hyp	Ref	Expression
1		ttctr	⊢ Tr TC+ 𝐴
2		ttctrid	⊢ ( Tr TC+ 𝐴 → TC+ TC+ 𝐴 = TC+ 𝐴 )
3	1 2	ax-mp	⊢ TC+ TC+ 𝐴 = TC+ 𝐴