Metamath Proof Explorer

Theorem finresfin

Description: The restriction of a finite set is finite. (Contributed by Alexander van der Vekens, 3-Jan-2018)

Ref Expression
Assertion finresfin 
|- ( E e. Fin -> ( E |` B ) e. Fin )

Proof

Step Hyp Ref Expression
1 resss 
 |-  ( E |` B ) C_ E
2 ssfi 
 |-  ( ( E e. Fin /\ ( E |` B ) C_ E ) -> ( E |` B ) e. Fin )
3 1 2 mpan2 
 |-  ( E e. Fin -> ( E |` B ) e. Fin )