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Theorem n0el 26710
 Description: Negated membership of the empty set in another class. (Contributed by Rodolfo Medina, 25-Sep-2010.)
Assertion
Ref Expression
n0el
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem n0el
StepHypRef Expression
1 df-ral 2712 . 2
2 df-ex 1552 . . 3
32ralbii 2731 . 2
4 alnex 1553 . . 3
5 imnan 413 . . . 4
65albii 1576 . . 3
7 0el 3646 . . . . 5
8 df-rex 2713 . . . . 5
97, 8bitri 242 . . . 4
109notbii 289 . . 3
114, 6, 103bitr4ri 271 . 2
121, 3, 113bitr4ri 271 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360  wal 1550  wex 1551   wcel 1726  wral 2707  wrex 2708  c0 3630 This theorem is referenced by:  prter2  26732 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-v 2960  df-dif 3325  df-nul 3631
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