Theorem ssttctr

Description: Transitivity of A C_ TC+ B relationship. (Contributed by Matthew House, 6-Apr-2026)

	Ref	Expression
Assertion	ssttctr	⊢ ( ( 𝐴 ⊆ TC+ 𝐵 ∧ 𝐵 ⊆ TC+ 𝐶 ) → 𝐴 ⊆ TC+ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		ttcss	⊢ ( 𝐵 ⊆ TC+ 𝐶 → TC+ 𝐵 ⊆ TC+ 𝐶 )
2		sstr	⊢ ( ( 𝐴 ⊆ TC+ 𝐵 ∧ TC+ 𝐵 ⊆ TC+ 𝐶 ) → 𝐴 ⊆ TC+ 𝐶 )
3	1 2	sylan2	⊢ ( ( 𝐴 ⊆ TC+ 𝐵 ∧ 𝐵 ⊆ TC+ 𝐶 ) → 𝐴 ⊆ TC+ 𝐶 )