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Theorem resid 4923
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 3150 . 2  |-  dom  A  C_ 
_V
2 relssres 4905 . 2  |-  ( ( Rel  A  /\  dom  A 
C_  _V )  ->  ( A  |`  _V )  =  A )
31, 2mpan2 422 1  |-  ( Rel 
A  ->  ( A  |` 
_V )  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1335   _Vcvv 2712    C_ wss 3102   dom cdm 4587    |` cres 4589   Rel wrel 4592
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-14 2131  ax-ext 2139  ax-sep 4083  ax-pow 4136  ax-pr 4170
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rex 2441  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-pw 3545  df-sn 3566  df-pr 3567  df-op 3569  df-br 3967  df-opab 4027  df-xp 4593  df-rel 4594  df-dm 4597  df-res 4599
This theorem is referenced by: (None)
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