Theorem mndtccat

Description: The function value is a category. (Contributed by Zhi Wang, 22-Sep-2024)

	Ref	Expression
Hypotheses	mndtccat.c	|- ( ph -> C = ( MndToCat ` M ) )
	mndtccat.m	|- ( ph -> M e. Mnd )
Assertion	mndtccat	|- ( ph -> C e. Cat )

Proof

Step	Hyp	Ref	Expression
1		mndtccat.c	|- ( ph -> C = ( MndToCat ` M ) )
2		mndtccat.m	|- ( ph -> M e. Mnd )
3	1 2	mndtccatid	|- ( ph -> ( C e. Cat /\ ( Id ` C ) = ( y e. ( Base ` C ) |-> ( 0g ` M ) ) ) )
4	3	simpld	|- ( ph -> C e. Cat )