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Theorem dfnul3 3787
Description: Alternate definition of the empty set. (Contributed by NM, 25-Mar-2004.)
Assertion
Ref Expression
dfnul3

Proof of Theorem dfnul3
StepHypRef Expression
1 pm3.24 882 . . . . 5
2 equid 1791 . . . . 5
31, 22th 239 . . . 4
43con1bii 331 . . 3
54abbii 2591 . 2
6 dfnul2 3786 . 2
7 df-rab 2816 . 2
85, 6, 73eqtr4i 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:  difidALT  3897  kmlem3  8553
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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