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Theorem elnev 27741
 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 2805 . 2
2 df-v 2803 . . . . 5
32eqeq2i 2306 . . . 4
4 equid 1662 . . . . . . 7
54tbt 333 . . . . . 6
65albii 1556 . . . . 5
7 alnex 1533 . . . . 5
8 abbi 2406 . . . . 5
96, 7, 83bitr3ri 267 . . . 4
103, 9bitri 240 . . 3
1110necon2abii 2514 . 2
121, 11bitri 240 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 176  wal 1530  wex 1531   wceq 1632   wcel 1696  cab 2282   wne 2459  cvv 2801 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-ne 2461  df-v 2803
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