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Theorem exists1 2245
 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 4217. (Contributed by NM, 5-Apr-2004.)
Assertion
Ref Expression
exists1
Distinct variable group:   ,

Proof of Theorem exists1
StepHypRef Expression
1 df-eu 2160 . 2
2 equid 1662 . . . . . 6
32tbt 333 . . . . 5
4 bicom 191 . . . . 5
53, 4bitri 240 . . . 4
65albii 1556 . . 3
76exbii 1572 . 2
8 nfae 1907 . . 3
9819.9 1795 . 2
101, 7, 93bitr2i 264 1
 Colors of variables: wff set class Syntax hints:   wb 176  wal 1530  wex 1531   wceq 1632  weu 2156 This theorem is referenced by:  exists2  2246 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 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535  df-eu 2160
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