Theorem ttctr2

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

	Ref	Expression
Assertion	ttctr2	⊢ ( 𝐴 ∈ TC+ 𝐵 → 𝐴 ⊆ TC+ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		ttctr	⊢ Tr TC+ 𝐵
2		trss	⊢ ( Tr TC+ 𝐵 → ( 𝐴 ∈ TC+ 𝐵 → 𝐴 ⊆ TC+ 𝐵 ) )
3	1 2	ax-mp	⊢ ( 𝐴 ∈ TC+ 𝐵 → 𝐴 ⊆ TC+ 𝐵 )