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Theorem euor2 2313
 Description: Introduce or eliminate a disjunct in a uniqueness quantifier. (Contributed by NM, 21-Oct-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) (Proof shortened by Wolf Lammen, 27-Dec-2018.)
Assertion
Ref Expression
euor2

Proof of Theorem euor2
StepHypRef Expression
1 nfe1 1894 . . 3
21nfn 1960 . 2
3 19.8a 1912 . . . 4
43con3i 140 . . 3
5 biorf 406 . . . 4
65bicomd 204 . . 3
74, 6syl 17 . 2
82, 7eubid 2287 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wo 369  wex 1657  weu 2269 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909 This theorem depends on definitions:  df-bi 188  df-or 371  df-ex 1658  df-nf 1662  df-eu 2273 This theorem is referenced by:  reuun2  3756
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