Metamath Proof Explorer


Theorem ttctr2

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

Ref Expression
Assertion ttctr2 Could not format assertion : No typesetting found for |- ( A e. TC+ B -> A C_ TC+ B ) with typecode |-

Proof

Step Hyp Ref Expression
1 ttctr Could not format Tr TC+ B : No typesetting found for |- Tr TC+ B with typecode |-
2 trss Could not format ( Tr TC+ B -> ( A e. TC+ B -> A C_ TC+ B ) ) : No typesetting found for |- ( Tr TC+ B -> ( A e. TC+ B -> A C_ TC+ B ) ) with typecode |-
3 1 2 ax-mp Could not format ( A e. TC+ B -> A C_ TC+ B ) : No typesetting found for |- ( A e. TC+ B -> A C_ TC+ B ) with typecode |-