Theorem fisuppfi

Description: A function on a finite set is finitely supported. (Contributed by Mario Carneiro, 20-Jun-2015)

	Ref	Expression
Hypotheses	fisuppfi.1	|- ( ph -> A e. Fin )
	fisuppfi.2	|- ( ph -> F : A --> B )
Assertion	fisuppfi	|- ( ph -> ( `' F " C ) e. Fin )

Proof

Step	Hyp	Ref	Expression
1		fisuppfi.1	|- ( ph -> A e. Fin )
2		fisuppfi.2	|- ( ph -> F : A --> B )
3		cnvimass	|- ( `' F " C ) C_ dom F
4	3 2	fssdm	|- ( ph -> ( `' F " C ) C_ A )
5	1 4	ssfid	|- ( ph -> ( `' F " C ) e. Fin )