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Theorem dfnul2 3786
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 3785 . . . 4
21eleq2i 2535 . . 3
3 eldif 3485 . . 3
4 eqid 2457 . . . . 5
5 pm3.24 882 . . . . 5
64, 52th 239 . . . 4
76con2bii 332 . . 3
82, 3, 73bitri 271 . 2
98abbi2i 2590 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442   cvv 3109  \cdif 3472   c0 3784
This theorem is referenced by:  dfnul3  3787  rab0  3806  iotanul  5571  avril1  25171
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-v 3111  df-dif 3478  df-nul 3785
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