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Theorem dfnul2 3364
 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 3363 . . . 4
21eleq2i 2317 . . 3
3 eldif 3088 . . 3
4 eqid 2253 . . . . 5
5 pm3.24 857 . . . . 5
64, 52th 232 . . . 4
76con2bii 324 . . 3
82, 3, 73bitri 264 . 2
98abbi2i 2360 1
 Colors of variables: wff set class Syntax hints:   wn 5   wa 360   wceq 1619   wcel 1621  cab 2239  cvv 2727   cdif 3075  c0 3362 This theorem is referenced by:  dfnul3  3365  rab0  3382  iotanul  6158  avril1  20666 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-dif 3081  df-nul 3363
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