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Theorem reuun2 3780
Description: Transfer uniqueness to a smaller or larger class. (Contributed by NM, 21-Oct-2005.)
Assertion
Ref Expression
reuun2
Distinct variable groups:   ,   ,

Proof of Theorem reuun2
StepHypRef Expression
1 df-rex 2813 . . 3
2 euor2 2333 . . 3
31, 2sylnbi 306 . 2
4 df-reu 2814 . . 3
5 elun 3644 . . . . . 6
65anbi1i 695 . . . . 5
7 andir 868 . . . . . 6
8 orcom 387 . . . . . 6
97, 8bitri 249 . . . . 5
106, 9bitri 249 . . . 4
1110eubii 2306 . . 3
124, 11bitri 249 . 2
13 df-reu 2814 . 2
143, 12, 133bitr4g 288 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369  E.wex 1612  e.wcel 1818  E!weu 2282  E.wrex 2808  E!wreu 2809  u.cun 3473
This theorem is referenced by:  hdmap14lem4a  37601
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-reu 2814  df-v 3111  df-un 3480
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