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Theorem resex 5178
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 5177 . 2  |-  ( A  e.  _V  ->  ( A  |`  B )  e. 
_V )
31, 2ax-mp 8 1  |-  ( A  |`  B )  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1725   _Vcvv 2948    |` cres 4872
This theorem is referenced by:  tfrlem9a  6639  domunsncan  7200  sbthlem10  7218  mapunen  7268  php3  7285  ssfi  7321  marypha1lem  7430  infdifsn  7603  ackbij2lem3  8113  fin1a2lem7  8278  hashf1lem2  11697  ramub2  13374  resf1st  14083  resf2nd  14084  funcres  14085  znval  16808  znle  16809  usgrafis  21421  cusgrasize  21479  hhssva  22751  hhsssm  22752  hhssnm  22753  hhshsslem1  22759  subfacp1lem3  24860  subfacp1lem5  24862  dfrdg2  25415  nofulllem5  25653  tfrqfree  25788  mbfresfi  26243  sdclem2  26437  diophrex  26825  rexrabdioph  26845  2rexfrabdioph  26847  3rexfrabdioph  26848  4rexfrabdioph  26849  6rexfrabdioph  26850  7rexfrabdioph  26851  rmydioph  27076  rmxdioph  27078  expdiophlem2  27084
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-ss 3326  df-res 4882
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