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Theorem euor2 2348
 Description: Introduce or eliminate a disjunct in a uniqueness quantifier. (Contributed by NM, 21-Oct-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
euor2

Proof of Theorem euor2
StepHypRef Expression
1 nfe1 1747 . . 3
21nfn 1811 . 2
3 19.8a 1762 . . . 4
43con3i 129 . . 3
5 orel1 372 . . . 4
6 olc 374 . . . 4
75, 6impbid1 195 . . 3
84, 7syl 16 . 2
92, 8eubid 2287 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358  wex 1550  weu 2280 This theorem is referenced by:  reuun2  3616 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-11 1761 This theorem depends on definitions:  df-bi 178  df-or 360  df-tru 1328  df-ex 1551  df-nf 1554  df-eu 2284
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