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Theorem dmv 5072
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 3464 . 2  |-  dom  _V  C_ 
_V
2 dmi 5071 . . 3  |-  dom  _I  =  _V
3 ssv 3464 . . . 4  |-  _I  C_  _V
4 dmss 5056 . . . 4  |-  (  _I  C_  _V  ->  dom  _I  C_  dom  _V )
53, 4ax-mp 5 . . 3  |-  dom  _I  C_ 
dom  _V
62, 5eqsstr3i 3475 . 2  |-  _V  C_  dom  _V
71, 6eqssi 3460 1  |-  dom  _V  =  _V
Colors of variables: wff setvar class
Syntax hints:    = wceq 1455   _Vcvv 3057    C_ wss 3416    _I cid 4766   dom cdm 4856
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-9 1907  ax-10 1926  ax-11 1931  ax-12 1944  ax-13 2102  ax-ext 2442  ax-sep 4541  ax-nul 4550  ax-pr 4656
This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-3an 993  df-tru 1458  df-ex 1675  df-nf 1679  df-sb 1809  df-eu 2314  df-mo 2315  df-clab 2449  df-cleq 2455  df-clel 2458  df-nfc 2592  df-ne 2635  df-ral 2754  df-rex 2755  df-rab 2758  df-v 3059  df-dif 3419  df-un 3421  df-in 3423  df-ss 3430  df-nul 3744  df-if 3894  df-sn 3981  df-pr 3983  df-op 3987  df-br 4419  df-opab 4478  df-id 4771  df-xp 4862  df-rel 4863  df-dm 4866
This theorem is referenced by: (None)
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