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Theorem dmv 5018
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 3304 . 2  |-  dom  _V  C_ 
_V
2 dmi 5017 . . 3  |-  dom  _I  =  _V
3 ssv 3304 . . . 4  |-  _I  C_  _V
4 dmss 5002 . . . 4  |-  (  _I  C_  _V  ->  dom  _I  C_  dom  _V )
53, 4ax-mp 8 . . 3  |-  dom  _I  C_ 
dom  _V
62, 5eqsstr3i 3315 . 2  |-  _V  C_  dom  _V
71, 6eqssi 3300 1  |-  dom  _V  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1649   _Vcvv 2892    C_ wss 3256    _I cid 4427   dom cdm 4811
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361  ax-sep 4264  ax-nul 4272  ax-pr 4337
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2235  df-mo 2236  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-ral 2647  df-rex 2648  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-br 4147  df-opab 4201  df-id 4432  df-xp 4817  df-rel 4818  df-dm 4821
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