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Theorem snnzb 4038
 Description: A singleton is nonempty iff its argument is a set. (Contributed by Scott Fenton, 8-May-2018.)
Assertion
Ref Expression
snnzb

Proof of Theorem snnzb
StepHypRef Expression
1 snprc 4037 . . 3
2 df-ne 2646 . . . 4
32con2bii 332 . . 3
41, 3bitri 249 . 2
54con4bii 297 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 184   wceq 1370   wcel 1758   wne 2644  cvv 3068  c0 3735  csn 3975 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-v 3070  df-dif 3429  df-nul 3736  df-sn 3976 This theorem is referenced by:  frlmip  18312  rrxip  21010  elima4  27724
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