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Theorem dmv 5078
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 3361 . 2  |-  dom  _V  C_ 
_V
2 dmi 5077 . . 3  |-  dom  _I  =  _V
3 ssv 3361 . . . 4  |-  _I  C_  _V
4 dmss 5062 . . . 4  |-  (  _I  C_  _V  ->  dom  _I  C_  dom  _V )
53, 4ax-mp 8 . . 3  |-  dom  _I  C_ 
dom  _V
62, 5eqsstr3i 3372 . 2  |-  _V  C_  dom  _V
71, 6eqssi 3357 1  |-  dom  _V  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1652   _Vcvv 2949    C_ wss 3313    _I cid 4486   dom cdm 4871
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4323  ax-nul 4331  ax-pr 4396
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2703  df-rex 2704  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-sn 3813  df-pr 3814  df-op 3816  df-br 4206  df-opab 4260  df-id 4491  df-xp 4877  df-rel 4878  df-dm 4881
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