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Theorem snnzg 3723
Description: The singleton of a set is not empty. (Contributed by NM, 14-Dec-2008.)
Assertion
Ref Expression
snnzg  |-  ( A  e.  V  ->  { A }  =/=  (/) )

Proof of Theorem snnzg
StepHypRef Expression
1 snidg 3635 . 2  |-  ( A  e.  V  ->  A  e.  { A } )
2 ne0i 3443 . 2  |-  ( A  e.  { A }  ->  { A }  =/=  (/) )
31, 2syl 14 1  |-  ( A  e.  V  ->  { A }  =/=  (/) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2159    =/= wne 2359   (/)c0 3436   {csn 3606
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2170
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2175  df-cleq 2181  df-clel 2184  df-nfc 2320  df-ne 2360  df-v 2753  df-dif 3145  df-nul 3437  df-sn 3612
This theorem is referenced by:  snnz  3725  0nelop  4262
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