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Theorem dmresv 5322
Description: The domain of a universal restriction. (Contributed by NM, 14-May-2008.)
Assertion
Ref Expression
dmresv  |-  dom  ( A  |`  _V )  =  dom  A

Proof of Theorem dmresv
StepHypRef Expression
1 dmres 5160 . 2  |-  dom  ( A  |`  _V )  =  ( _V  i^i  dom  A )
2 incom 3526 . 2  |-  ( _V 
i^i  dom  A )  =  ( dom  A  i^i  _V )
3 inv1 3647 . 2  |-  ( dom 
A  i^i  _V )  =  dom  A
41, 2, 33eqtri 2460 1  |-  dom  ( A  |`  _V )  =  dom  A
Colors of variables: wff set class
Syntax hints:    = wceq 1652   _Vcvv 2949    i^i cin 3312   dom cdm 4871    |` cres 4873
This theorem is referenced by:  fidomdm  7381  dmct  24099
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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4323  ax-nul 4331  ax-pr 4396
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2703  df-rex 2704  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-sn 3813  df-pr 3814  df-op 3816  df-br 4206  df-opab 4260  df-xp 4877  df-dm 4881  df-res 4883
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