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Theorem dfnul2 3220
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 3219 . . . 4  (/)  _V  \  _V
21eleq2i 2101 . . 3  (/)  _V  \  _V
3 eldif 2921 . . 3  _V  \  _V  _V  _V
4 pm3.24 626 . . . 4  _V  _V
5 eqid 2037 . . . . 5
65notnoti 573 . . . 4
74, 62false 616 . . 3  _V  _V
82, 3, 73bitri 195 . 2  (/)
98abbi2i 2149 1  (/)  {  |  }
Colors of variables: wff set class
Syntax hints:   wn 3   wa 97   wceq 1242   wcel 1390   {cab 2023   _Vcvv 2551    \ cdif 2908   (/)c0 3218
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 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-dif 2914  df-nul 3219
This theorem is referenced by:  dfnul3  3221  rab0  3240  iotanul  4825
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