Metamath Proof Explorer


Theorem ssttctr

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

Ref Expression
Assertion ssttctr Could not format assertion : No typesetting found for |- ( ( A C_ TC+ B /\ B C_ TC+ C ) -> A C_ TC+ C ) with typecode |-

Proof

Step Hyp Ref Expression
1 ttcss Could not format ( B C_ TC+ C -> TC+ B C_ TC+ C ) : No typesetting found for |- ( B C_ TC+ C -> TC+ B C_ TC+ C ) with typecode |-
2 sstr Could not format ( ( A C_ TC+ B /\ TC+ B C_ TC+ C ) -> A C_ TC+ C ) : No typesetting found for |- ( ( A C_ TC+ B /\ TC+ B C_ TC+ C ) -> A C_ TC+ C ) with typecode |-
3 1 2 sylan2 Could not format ( ( A C_ TC+ B /\ B C_ TC+ C ) -> A C_ TC+ C ) : No typesetting found for |- ( ( A C_ TC+ B /\ B C_ TC+ C ) -> A C_ TC+ C ) with typecode |-