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Theorem snnzb 4094
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 4093 . . 3
2 df-ne 2654 . . . 4
32con2bii 332 . . 3
41, 3bitri 249 . 2
54con4bii 297 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  =wceq 1395  e.wcel 1818  =/=wne 2652   cvv 3109   c0 3784  {csn 4029
This theorem is referenced by:  elima4  29209
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-nul 3785  df-sn 4030
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