Theorem fsuppimpd

Description: A finitely supported function is a function with a finite support. (Contributed by AV, 6-Jun-2019)

	Ref	Expression
Hypothesis	fsuppimpd.f	|- ( ph -> F finSupp Z )
Assertion	fsuppimpd	|- ( ph -> ( F supp Z ) e. Fin )

Proof

Step	Hyp	Ref	Expression
1		fsuppimpd.f	|- ( ph -> F finSupp Z )
2		fsuppimp	|- ( F finSupp Z -> ( Fun F /\ ( F supp Z ) e. Fin ) )
3	2	simprd	|- ( F finSupp Z -> ( F supp Z ) e. Fin )
4	1 3	syl	|- ( ph -> ( F supp Z ) e. Fin )