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Theorem resex 5315
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 5314 . 2  |-  ( A  e.  _V  ->  ( A  |`  B )  e. 
_V )
31, 2ax-mp 5 1  |-  ( A  |`  B )  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1767   _Vcvv 3113    |` cres 5001
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-in 3483  df-ss 3490  df-res 5011
This theorem is referenced by:  tfrlem9a  7052  domunsncan  7614  sbthlem10  7633  mapunen  7683  php3  7700  ssfi  7737  marypha1lem  7889  infdifsn  8069  ackbij2lem3  8617  fin1a2lem7  8782  hashf1lem2  12467  ramub2  14387  resf1st  15117  resf2nd  15118  funcres  15119  lubfval  15461  glbfval  15474  znval  18339  znle  18340  usgrafis  24091  cusgrasize  24154  wlknwwlknvbij  24416  clwwlkvbij  24477  hhssva  25851  hhsssm  25852  hhssnm  25853  hhshsslem1  25859  eulerpartlemt  27950  eulerpartgbij  27951  eulerpart  27961  fibp1  27980  subfacp1lem3  28266  subfacp1lem5  28268  dfrdg2  28805  nofulllem5  29043  tfrqfree  29178  finixpnum  29615  mbfresfi  29638  sdclem2  29838  diophrex  30313  rexrabdioph  30331  2rexfrabdioph  30333  3rexfrabdioph  30334  4rexfrabdioph  30335  6rexfrabdioph  30336  7rexfrabdioph  30337  rmydioph  30560  rmxdioph  30562  expdiophlem2  30568  fouriersw  31532  uhgres  31848
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