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Theorem dmsn0 5340
 Description: The domain of the singleton of the empty set is empty. (Contributed by NM, 30-Jan-2004.)
Assertion
Ref Expression
dmsn0

Proof of Theorem dmsn0
StepHypRef Expression
1 0nelxp 4909 . 2
2 dmsnn0 5338 . . 3
32necon2bbii 2662 . 2
41, 3mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1653   wcel 1726  cvv 2958  c0 3630  csn 3816   cxp 4879   cdm 4881 This theorem is referenced by:  cnvsn0  5341  dmsnopss  5345  1st0  6356  2nd0  6357 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-xp 4887  df-dm 4891
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