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Theorem dmv 4622
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 3035 . 2 dom V ⊆ V
2 dmi 4621 . . 3 dom I = V
3 ssv 3035 . . . 4 I ⊆ V
4 dmss 4605 . . . 4 ( I ⊆ V → dom I ⊆ dom V)
53, 4ax-mp 7 . . 3 dom I ⊆ dom V
62, 5eqsstr3i 3046 . 2 V ⊆ dom V
71, 6eqssi 3030 1 dom V = V
Colors of variables: wff set class
Syntax hints:   = wceq 1287  Vcvv 2615  wss 2988   I cid 4091  dom cdm 4413
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-14 1448  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-sep 3934  ax-pow 3986  ax-pr 4012
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-eu 1948  df-mo 1949  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360  df-rex 2361  df-v 2617  df-un 2992  df-in 2994  df-ss 3001  df-pw 3417  df-sn 3437  df-pr 3438  df-op 3440  df-br 3823  df-opab 3877  df-id 4096  df-xp 4419  df-rel 4420  df-dm 4423
This theorem is referenced by: (None)
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