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Theorem elnev 26805
 Description: Any set that contains one element less than the universe is not equal to it. (Contributed by Andrew Salmon, 16-Jun-2011.)
Assertion
Ref Expression
elnev
Distinct variable group:   ,

Proof of Theorem elnev
StepHypRef Expression
1 isset 2731 . 2
2 df-v 2729 . . . . 5
32eqeq2i 2263 . . . 4
4 equid 1818 . . . . . . 7
54tbt 335 . . . . . 6
65albii 1554 . . . . 5
7 alnex 1569 . . . . 5
8 abbi 2359 . . . . 5
96, 7, 83bitr3ri 269 . . . 4
103, 9bitri 242 . . 3
1110necon2abii 2467 . 2
121, 11bitri 242 1
 Colors of variables: wff set class Syntax hints:   wn 5   wb 178  wal 1532  wex 1537   wceq 1619   wcel 1621  cab 2239   wne 2412  cvv 2727 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-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-ne 2414  df-v 2729
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