Theorem psrbagf

Description: A finite bag is a function. (Contributed by Mario Carneiro, 29-Dec-2014)

	Ref	Expression
Hypothesis	psrbag.d	|- D = { f e. ( NN0 ^m I ) | ( `' f " NN ) e. Fin }
Assertion	psrbagf	|- ( ( I e. V /\ F e. D ) -> F : I --> NN0 )

Proof

Step	Hyp	Ref	Expression
1		psrbag.d	|- D = { f e. ( NN0 ^m I ) | ( `' f " NN ) e. Fin }
2	1	psrbag	|- ( I e. V -> ( F e. D <-> ( F : I --> NN0 /\ ( `' F " NN ) e. Fin ) ) )
3	2	simprbda	|- ( ( I e. V /\ F e. D ) -> F : I --> NN0 )