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Theorem reuhypd 4679
 Description: A theorem useful for eliminating the restricted existential uniqueness hypotheses in riotaxfrd 6288. (Contributed by NM, 16-Jan-2012.)
Hypotheses
Ref Expression
reuhypd.1
reuhypd.2
Assertion
Ref Expression
reuhypd
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem reuhypd
StepHypRef Expression
1 reuhypd.1 . . . . 5
2 elex 3118 . . . . 5
31, 2syl 16 . . . 4
4 eueq 3271 . . . 4
53, 4sylib 196 . . 3
6 eleq1 2529 . . . . . . 7
71, 6syl5ibrcom 222 . . . . . 6
87pm4.71rd 635 . . . . 5
9 reuhypd.2 . . . . . . 7
1093expa 1196 . . . . . 6
1110pm5.32da 641 . . . . 5
128, 11bitr4d 256 . . . 4
1312eubidv 2304 . . 3
145, 13mpbid 210 . 2
15 df-reu 2814 . 2
1614, 15sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  E!weu 2282  E!wreu 2809   cvv 3109 This theorem is referenced by:  reuhyp  4680  riotaocN  34934 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-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-reu 2814  df-v 3111
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