Metamath Proof Explorer


Theorem ttcel2

Description: Elements turn into subclasses upon taking transitive closures. (Contributed by Matthew House, 6-Apr-2026)

Ref Expression
Assertion ttcel2 Could not format assertion : No typesetting found for |- ( A e. B -> TC+ A C_ TC+ B ) with typecode |-

Proof

Step Hyp Ref Expression
1 ttcid Could not format B C_ TC+ B : No typesetting found for |- B C_ TC+ B with typecode |-
2 1 sseli Could not format ( A e. B -> A e. TC+ B ) : No typesetting found for |- ( A e. B -> A e. TC+ B ) with typecode |-
3 ttcel Could not format ( A e. TC+ B -> TC+ A C_ TC+ B ) : No typesetting found for |- ( A e. TC+ B -> TC+ A C_ TC+ B ) with typecode |-
4 2 3 syl Could not format ( A e. B -> TC+ A C_ TC+ B ) : No typesetting found for |- ( A e. B -> TC+ A C_ TC+ B ) with typecode |-