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Theorem reuun2 3538
 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 2620 . . 3
2 euor2 2272 . . 3
31, 2sylnbi 297 . 2
4 df-reu 2621 . . 3
5 elun 3220 . . . . . 6
65anbi1i 676 . . . . 5
7 andir 838 . . . . . 6
8 orcom 376 . . . . . 6
97, 8bitri 240 . . . . 5
106, 9bitri 240 . . . 4
1110eubii 2213 . . 3
124, 11bitri 240 . 2
13 df-reu 2621 . 2
143, 12, 133bitr4g 279 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176   wo 357   wa 358  wex 1541   wcel 1710  weu 2204  wrex 2615  wreu 2616   cun 3207 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-reu 2621  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214 This theorem is referenced by: (None)
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