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Theorem dfnul2 3203
Description: Alternate definition of the empty set. Definition 5.14 of [TakeutiZaring] p. 20. (Contributed by NM, 26-Dec-1996.)
Assertion
Ref Expression
dfnul2  (/)  {  |  }

Proof of Theorem dfnul2
StepHypRef Expression
1 df-nul 3202 . . . 4  (/)  _V  \  _V
21eleq2i 2086 . . 3  (/)  _V  \  _V
3 eldif 2904 . . 3  _V  \  _V  _V  _V
4 pm3.24 614 . . . 4  _V  _V
5 eqid 2022 . . . . 5
65notnoti 561 . . . 4
74, 62false 604 . . 3  _V  _V
82, 3, 73bitri 195 . 2  (/)
98abbi2i 2134 1  (/)  {  |  }
Colors of variables: wff set class
Syntax hints:   wn 3   wa 97   wceq 1228   wcel 1374   {cab 2008   _Vcvv 2535    \ cdif 2891   (/)c0 3201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-dif 2897  df-nul 3202
This theorem is referenced by:  dfnul3  3204  rab0  3223  iotanul  4809
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