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Theorem dmv 4894
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 3198 . 2  |-  dom  _V  C_ 
_V
2 dmi 4893 . . 3  |-  dom  _I  =  _V
3 ssv 3198 . . . 4  |-  _I  C_  _V
4 dmss 4878 . . . 4  |-  (  _I  C_  _V  ->  dom  _I  C_  dom  _V )
53, 4ax-mp 8 . . 3  |-  dom  _I  C_ 
dom  _V
62, 5eqsstr3i 3209 . 2  |-  _V  C_  dom  _V
71, 6eqssi 3195 1  |-  dom  _V  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1623   _Vcvv 2788    C_ wss 3152    _I cid 4304   dom cdm 4689
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-id 4309  df-xp 4695  df-rel 4696  df-dm 4699
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