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Theorem elnev 36789
 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 3049 . 2
2 df-v 3047 . . . . 5
32eqeq2i 2463 . . . 4
4 equid 1855 . . . . . . 7
54tbt 346 . . . . . 6
65albii 1691 . . . . 5
7 alnex 1665 . . . . 5
8 abbi 2565 . . . . 5
96, 7, 83bitr3ri 280 . . . 4
103, 9bitri 253 . . 3
1110necon2abii 2674 . 2
121, 11bitri 253 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 188  wal 1442   wceq 1444  wex 1663   wcel 1887  cab 2437   wne 2622  cvv 3045 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-ne 2624  df-v 3047 This theorem is referenced by: (None)
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