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Theorem exists1 2388
Description: Two ways to express "only one thing exists." The left-hand side requires only one variable to express this. Both sides are false in set theory; see theorem dtru 4643. (Contributed by NM, 5-Apr-2004.)
Assertion
Ref Expression
exists1
Distinct variable group:   ,

Proof of Theorem exists1
StepHypRef Expression
1 df-eu 2286 . 2
2 equid 1791 . . . . . 6
32tbt 344 . . . . 5
4 bicom 200 . . . . 5
53, 4bitri 249 . . . 4
65albii 1640 . . 3
76exbii 1667 . 2
8 nfae 2056 . . 3
9819.9 1893 . 2
101, 7, 93bitr2i 273 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  A.wal 1393  E.wex 1612  E!weu 2282
This theorem is referenced by:  exists2  2389
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286
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