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Theorem reuhypd 4644
 Description: A theorem useful for eliminating the restricted existential uniqueness hypotheses in riotaxfrd 6293. (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 3090 . . . . 5
31, 2syl 17 . . . 4
4 eueq 3243 . . . 4
53, 4sylib 199 . . 3
6 eleq1 2494 . . . . . . 7
71, 6syl5ibrcom 225 . . . . . 6
87pm4.71rd 639 . . . . 5
9 reuhypd.2 . . . . . . 7
1093expa 1205 . . . . . 6
1110pm5.32da 645 . . . . 5
128, 11bitr4d 259 . . . 4
1312eubidv 2286 . . 3
145, 13mpbid 213 . 2
15 df-reu 2782 . 2
1614, 15sylibr 215 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   w3a 982   wceq 1437   wcel 1868  weu 2265  wreu 2777  cvv 3081 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-eu 2269  df-mo 2270  df-clab 2408  df-cleq 2414  df-clel 2417  df-reu 2782  df-v 3083 This theorem is referenced by:  reuhyp  4645  riotaocN  32693
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