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Theorem reuhypd 4752
 Description: A theorem useful for eliminating the restricted existential uniqueness hypotheses in riotaxfrd 6583. (Contributed by NM, 16-Jan-2012.)
Hypotheses
Ref Expression
reuhypd.1
reuhypd.2
Assertion
Ref Expression
reuhypd
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   (,)   ()   ()

Proof of Theorem reuhypd
StepHypRef Expression
1 reuhypd.1 . . . . 5
2 elex 2966 . . . . 5
31, 2syl 16 . . . 4
4 eueq 3108 . . . 4
53, 4sylib 190 . . 3
6 eleq1 2498 . . . . . . 7
71, 6syl5ibrcom 215 . . . . . 6
87pm4.71rd 618 . . . . 5
9 reuhypd.2 . . . . . . 7
1093expa 1154 . . . . . 6
1110pm5.32da 624 . . . . 5
128, 11bitr4d 249 . . . 4
1312eubidv 2291 . . 3
145, 13mpbid 203 . 2
15 df-reu 2714 . 2
1614, 15sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937   wceq 1653   wcel 1726  weu 2283  wreu 2709  cvv 2958 This theorem is referenced by:  reuhyp  4753  riotaocN  30069 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-reu 2714  df-v 2960
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