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Theorem dmv 5069
Description: The domain of the universe is the universe. (Contributed by NM, 8-Aug-2003.)
Assertion
Ref Expression
dmv  |-  dom  _V  =  _V

Proof of Theorem dmv
StepHypRef Expression
1 ssv 3484 . 2  |-  dom  _V  C_ 
_V
2 dmi 5068 . . 3  |-  dom  _I  =  _V
3 ssv 3484 . . . 4  |-  _I  C_  _V
4 dmss 5053 . . . 4  |-  (  _I  C_  _V  ->  dom  _I  C_  dom  _V )
53, 4ax-mp 5 . . 3  |-  dom  _I  C_ 
dom  _V
62, 5eqsstr3i 3495 . 2  |-  _V  C_  dom  _V
71, 6eqssi 3480 1  |-  dom  _V  =  _V
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437   _Vcvv 3080    C_ wss 3436    _I cid 4763   dom cdm 4853
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-eu 2273  df-mo 2274  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-id 4768  df-xp 4859  df-rel 4860  df-dm 4863
This theorem is referenced by: (None)
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