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Theorem reuun2 3733
 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 2801 . . 3
2 euor2 2319 . . 3
31, 2sylnbi 306 . 2
4 df-reu 2802 . . 3
5 elun 3597 . . . . . 6
65anbi1i 695 . . . . 5
7 andir 863 . . . . . 6
8 orcom 387 . . . . . 6
97, 8bitri 249 . . . . 5
106, 9bitri 249 . . . 4
1110eubii 2285 . . 3
124, 11bitri 249 . 2
13 df-reu 2802 . 2
143, 12, 133bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wo 368   wa 369  wex 1587   wcel 1758  weu 2260  wrex 2796  wreu 2797   cun 3426 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2264  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-rex 2801  df-reu 2802  df-v 3072  df-un 3433 This theorem is referenced by:  hdmap14lem4a  35827
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