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Theorem dfnul2 3622
 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 3621 . . . 4
21eleq2i 2499 . . 3
3 eldif 3322 . . 3
4 eqid 2435 . . . . 5
5 pm3.24 853 . . . . 5
64, 52th 231 . . . 4
76con2bii 323 . . 3
82, 3, 73bitri 263 . 2
98abbi2i 2546 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 359   wceq 1652   wcel 1725  cab 2421  cvv 2948   cdif 3309  c0 3620 This theorem is referenced by:  dfnul3  3623  rab0  3640  iotanul  5425  avril1  21749 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-dif 3315  df-nul 3621
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