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Theorem resid 5088
Description: Any relation restricted to the universe is itself. (Contributed by NM, 16-Mar-2004.)
Assertion
Ref Expression
resid  |-  ( Rel 
A  ->  ( A  |` 
_V )  =  A )

Proof of Theorem resid
StepHypRef Expression
1 ssv 3274 . 2  |-  dom  A  C_ 
_V
2 relssres 5074 . 2  |-  ( ( Rel  A  /\  dom  A 
C_  _V )  ->  ( A  |`  _V )  =  A )
31, 2mpan2 652 1  |-  ( Rel 
A  ->  ( A  |` 
_V )  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1642   _Vcvv 2864    C_ wss 3228   dom cdm 4771    |` cres 4773   Rel wrel 4776
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-sep 4222  ax-nul 4230  ax-pr 4295
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-br 4105  df-opab 4159  df-xp 4777  df-rel 4778  df-dm 4781  df-res 4783
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