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Theorem resex 4860
Description: The restriction of a set is a set. (Contributed by Jeff Madsen, 19-Jun-2011.)
Hypothesis
Ref Expression
resex.1  |-  A  e. 
_V
Assertion
Ref Expression
resex  |-  ( A  |`  B )  e.  _V

Proof of Theorem resex
StepHypRef Expression
1 resex.1 . 2  |-  A  e. 
_V
2 resexg 4859 . 2  |-  ( A  e.  _V  ->  ( A  |`  B )  e. 
_V )
31, 2ax-mp 5 1  |-  ( A  |`  B )  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1480   _Vcvv 2686    |` cres 4541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077  df-ss 3084  df-res 4551
This theorem is referenced by:  sbthlemi10  6854  finomni  7012  ctinf  11954
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