Metamath Proof Explorer


Theorem elttctr

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

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

Proof

Step Hyp Ref Expression
1 ttcel Could not format ( B e. TC+ C -> TC+ B C_ TC+ C ) : No typesetting found for |- ( B e. TC+ C -> TC+ B C_ TC+ C ) with typecode |-
2 1 sseld Could not format ( B e. TC+ C -> ( A e. TC+ B -> A e. TC+ C ) ) : No typesetting found for |- ( B e. TC+ C -> ( A e. TC+ B -> A e. TC+ C ) ) with typecode |-
3 2 impcom Could not format ( ( A e. TC+ B /\ B e. TC+ C ) -> A e. TC+ C ) : No typesetting found for |- ( ( A e. TC+ B /\ B e. TC+ C ) -> A e. TC+ C ) with typecode |-