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Theorem exists1 2369
 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 4382. (Contributed by NM, 5-Apr-2004.)
Assertion
Ref Expression
exists1
Distinct variable group:   ,

Proof of Theorem exists1
StepHypRef Expression
1 df-eu 2284 . 2
2 equid 1688 . . . . . 6
32tbt 334 . . . . 5
4 bicom 192 . . . . 5
53, 4bitri 241 . . . 4
65albii 1575 . . 3
76exbii 1592 . 2
8 nfae 2042 . . 3
9819.9 1797 . 2
101, 7, 93bitr2i 265 1
 Colors of variables: wff set class Syntax hints:   wb 177  wal 1549  wex 1550  weu 2280 This theorem is referenced by:  exists2  2370 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-eu 2284
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