Metamath Proof Explorer

Theorem resexg

Description: The restriction of a set is a set. (Contributed by NM, 28-Mar-1998) (Proof shortened by Andrew Salmon, 27-Aug-2011)

Ref Expression
Assertion resexg 
|- ( A e. V -> ( A |` B ) e. _V )

Proof

Step Hyp Ref Expression
1 resss 
 |-  ( A |` B ) C_ A
2 ssexg 
 |-  ( ( ( A |` B ) C_ A /\ A e. V ) -> ( A |` B ) e. _V )
3 1 2 mpan 
 |-  ( A e. V -> ( A |` B ) e. _V )