Metamath Proof Explorer


Theorem ttcexbi

Description: A class is a set iff its transitive closure is a set, assuming Transitive Containment. (Contributed by Matthew House, 6-Apr-2026)

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

Proof

Step Hyp Ref Expression
1 ttcexg Could not format ( A e. _V -> TC+ A e. _V ) : No typesetting found for |- ( A e. _V -> TC+ A e. _V ) with typecode |-
2 ttcexrg Could not format ( TC+ A e. _V -> A e. _V ) : No typesetting found for |- ( TC+ A e. _V -> A e. _V ) with typecode |-
3 1 2 impbii Could not format ( A e. _V <-> TC+ A e. _V ) : No typesetting found for |- ( A e. _V <-> TC+ A e. _V ) with typecode |-