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Metamath Proof Explorer

Theorem istermc3

Description: The predicate "is a terminal category". A terminal category is a thin category whose base set is equinumerous to 1o . Consider en1b , map1 , and euen1b . (Contributed by Zhi Wang, 16-Oct-2025)

		Ref	Expression
	Hypothesis	istermc.b	$⊢ B = {Base}_{C}$
	Assertion	istermc3	Could not format assertion : No typesetting found for \|- ( C e. TermCat <-> ( C e. ThinCat /\ B ~~ 1o ) ) with typecode \|-

Proof

Step	Hyp	Ref	Expression
1		istermc.b	$⊢ B = {Base}_{C}$
2	1	istermc	Could not format ( C e. TermCat <-> ( C e. ThinCat /\ E. x B = { x } ) ) : No typesetting found for \|- ( C e. TermCat <-> ( C e. ThinCat /\ E. x B = { x } ) ) with typecode \|-
3		en1	$⊢ B \approx 1_{𝑜} \leftrightarrow \exists x B = \{x\}$
4	3	anbi2i	$⊢ (C \in ThinCat \land B \approx 1_{𝑜}) \leftrightarrow (C \in ThinCat \land \exists x B = \{x\})$
5	2 4	bitr4i	Could not format ( C e. TermCat <-> ( C e. ThinCat /\ B ~~ 1o ) ) : No typesetting found for \|- ( C e. TermCat <-> ( C e. ThinCat /\ B ~~ 1o ) ) with typecode \|-