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Theorem rnsnn0 5479
 Description: The range of a singleton is nonzero iff the singleton argument is an ordered pair. (Contributed by NM, 14-Dec-2008.)
Assertion
Ref Expression
rnsnn0

Proof of Theorem rnsnn0
StepHypRef Expression
1 dmsnn0 5478 . 2
2 dm0rn0 5224 . . 3
32necon3bii 2725 . 2
41, 3bitri 249 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  e.wcel 1818  =/=wne 2652   cvv 3109   c0 3784  {csn 4029  X.cxp 5002  domcdm 5004  rancrn 5005 This theorem is referenced by:  2ndnpr  6805  2nd2val  6827 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010  df-cnv 5012  df-dm 5014  df-rn 5015
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