Metamath Proof Explorer


Theorem termcthind

Description: A terminal category is a thin category (deduction form). (Contributed by Zhi Wang, 16-Oct-2025)

Ref Expression
Hypothesis termcthind.c
|- ( ph -> C e. TermCat )
Assertion termcthind
|- ( ph -> C e. ThinCat )

Proof

Step Hyp Ref Expression
1 termcthind.c
 |-  ( ph -> C e. TermCat )
2 termcthin
 |-  ( C e. TermCat -> C e. ThinCat )
3 1 2 syl
 |-  ( ph -> C e. ThinCat )