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Theorem reuun2 3616
 Description: Transfer uniqueness to a smaller or larger class. (Contributed by NM, 21-Oct-2005.)
Assertion
Ref Expression
reuun2
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem reuun2
StepHypRef Expression
1 df-rex 2703 . . 3
2 euor2 2348 . . 3
31, 2sylnbi 298 . 2
4 df-reu 2704 . . 3
5 elun 3480 . . . . . 6
65anbi1i 677 . . . . 5
7 andir 839 . . . . . 6
8 orcom 377 . . . . . 6
97, 8bitri 241 . . . . 5
106, 9bitri 241 . . . 4
1110eubii 2289 . . 3
124, 11bitri 241 . 2
13 df-reu 2704 . 2
143, 12, 133bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359  wex 1550   wcel 1725  weu 2280  wrex 2698  wreu 2699   cun 3310 This theorem is referenced by:  hdmap14lem4a  32573 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  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-reu 2704  df-v 2950  df-un 3317
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