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Theorem resex 4786
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 4785 . 2  |-  ( A  e.  _V  ->  ( A  |`  B )  e. 
_V )
31, 2ax-mp 7 1  |-  ( A  |`  B )  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1445   _Vcvv 2633    |` cres 4469
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077  ax-sep 3978
This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-v 2635  df-in 3019  df-ss 3026  df-res 4479
This theorem is referenced by:  sbthlemi10  6755  finomni  6883
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