Metamath Proof Explorer


Theorem ttctr3

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

Ref Expression
Assertion ttctr3 Could not format assertion : No typesetting found for |- U. TC+ A C_ TC+ A with typecode |-

Proof

Step Hyp Ref Expression
1 ttctr Could not format Tr TC+ A : No typesetting found for |- Tr TC+ A with typecode |-
2 df-tr Could not format ( Tr TC+ A <-> U. TC+ A C_ TC+ A ) : No typesetting found for |- ( Tr TC+ A <-> U. TC+ A C_ TC+ A ) with typecode |-
3 1 2 mpbi Could not format U. TC+ A C_ TC+ A : No typesetting found for |- U. TC+ A C_ TC+ A with typecode |-