Metamath Proof Explorer


Theorem ttcss2

Description: The subclass relationship is inherited by transitive closures. (Contributed by Matthew House, 6-Apr-2026)

Ref Expression
Assertion ttcss2 Could not format assertion : No typesetting found for |- ( A C_ 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 sstr Could not format ( ( A C_ B /\ B C_ TC+ B ) -> A C_ TC+ B ) : No typesetting found for |- ( ( A C_ B /\ B C_ TC+ B ) -> A C_ TC+ B ) with typecode |-
3 1 2 mpan2 Could not format ( A C_ B -> A C_ TC+ B ) : No typesetting found for |- ( A C_ B -> A C_ TC+ B ) with typecode |-
4 ttcss Could not format ( A C_ TC+ B -> TC+ A C_ TC+ B ) : No typesetting found for |- ( A C_ TC+ B -> TC+ A C_ TC+ B ) with typecode |-
5 3 4 syl Could not format ( A C_ B -> TC+ A C_ TC+ B ) : No typesetting found for |- ( A C_ B -> TC+ A C_ TC+ B ) with typecode |-