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Theorem dfnul3 3204
Description: Alternate definition of the empty set. (Contributed by NM, 25-Mar-2004.)
Assertion
Ref Expression
dfnul3  (/)  {  |  }

Proof of Theorem dfnul3
StepHypRef Expression
1 equid 1571 . . . . 5
21notnoti 561 . . . 4
3 pm3.24 614 . . . 4
42, 32false 604 . . 3
54abbii 2135 . 2  {  |  }  {  |  }
6 dfnul2 3203 . 2  (/)  {  |  }
7 df-rab 2293 . 2  {  |  }  {  |  }
85, 6, 73eqtr4i 2052 1  (/)  {  |  }
Colors of variables: wff set class
Syntax hints:   wn 3   wa 97   wceq 1228   wcel 1374   {cab 2008   {crab 2288   (/)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-rab 2293  df-v 2537  df-dif 2897  df-nul 3202
This theorem is referenced by:  difidALT  3270
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