Metamath Proof Explorer


Theorem psrbagfOLD

Description: Obsolete version of psrbag as of 6-Aug-2024. (Contributed by Mario Carneiro, 29-Dec-2014) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis psrbag.d
|- D = { f e. ( NN0 ^m I ) | ( `' f " NN ) e. Fin }
Assertion psrbagfOLD
|- ( ( 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 )