Metamath Proof Explorer


Theorem ttcidm

Description: The transitive closure operation is idempotent. (Contributed by Matthew House, 6-Apr-2026)

Ref Expression
Assertion ttcidm Could not format assertion : No typesetting found for |- TC+ TC+ A = 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 ttctrid Could not format ( Tr TC+ A -> TC+ TC+ A = TC+ A ) : No typesetting found for |- ( Tr TC+ A -> TC+ TC+ A = TC+ A ) with typecode |-
3 1 2 ax-mp Could not format TC+ TC+ A = TC+ A : No typesetting found for |- TC+ TC+ A = TC+ A with typecode |-