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Theorem rab0 3223
Description: Any restricted class abstraction restricted to the empty set is empty. (Contributed by NM, 15-Oct-2003.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
rab0  {  (/)  |  }  (/)

Proof of Theorem rab0
StepHypRef Expression
1 noel 3205 . . . . 5  (/)
21intnanr 827 . . . 4  (/)
3 equid 1571 . . . . 5
43notnoti 561 . . . 4
52, 42false 604 . . 3  (/)
65abbii 2135 . 2  {  |  (/)  }  {  |  }
7 df-rab 2293 . 2  {  (/)  |  }  {  |  (/)  }
8 dfnul2 3203 . 2  (/)  {  |  }
96, 7, 83eqtr4i 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: (None)
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