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Theorem rab0 3806
 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 equid 1791 . . . . 5
2 noel 3788 . . . . . 6
32intnanr 915 . . . . 5
41, 32th 239 . . . 4
54con2bii 332 . . 3
65abbii 2591 . 2
7 df-rab 2816 . 2
8 dfnul2 3786 . 2
96, 7, 83eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  {crab 2811   c0 3784 This theorem is referenced by:  rabsnif  4099  supp0  6923  scott0  8325  psgnfval  16525  pmtrsn  16544  00lsp  17627  rrgval  17935  usgra0v  24371  vdgr0  24900 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-nul 3785
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