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Theorem resid 5181
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 3484 . 2  |-  dom  A  C_ 
_V
2 relssres 5161 . 2  |-  ( ( Rel  A  /\  dom  A 
C_  _V )  ->  ( A  |`  _V )  =  A )
31, 2mpan2 675 1  |-  ( Rel 
A  ->  ( A  |` 
_V )  =  A )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1437   _Vcvv 3080    C_ wss 3436   dom cdm 4853    |` cres 4855   Rel wrel 4858
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401  ax-sep 4546  ax-nul 4555  ax-pr 4660
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ne 2616  df-ral 2776  df-rex 2777  df-rab 2780  df-v 3082  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3912  df-sn 3999  df-pr 4001  df-op 4005  df-br 4424  df-opab 4483  df-xp 4859  df-rel 4860  df-dm 4863  df-res 4865
This theorem is referenced by: (None)
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