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Theorem reuhypd 4169
Description: A theorem useful for eliminating restricted existential uniqueness hypotheses. (Contributed by NM, 16-Jan-2012.)
Hypotheses
Ref Expression
reuhypd.1  C  C
reuhypd.2  C  C
Assertion
Ref Expression
reuhypd  C  C
Distinct variable groups:   ,   ,   , C   ,
Allowed substitution hints:   ()   (,)   ()    C()

Proof of Theorem reuhypd
StepHypRef Expression
1 reuhypd.1 . . . . 5  C  C
2 elex 2560 . . . . 5  C  _V
31, 2syl 14 . . . 4  C  _V
4 eueq 2706 . . . 4  _V
53, 4sylib 127 . . 3  C
6 eleq1 2097 . . . . . . 7  C  C
71, 6syl5ibrcom 146 . . . . . 6  C  C
87pm4.71rd 374 . . . . 5  C  C
9 reuhypd.2 . . . . . . 7  C  C
1093expa 1103 . . . . . 6  C  C
1110pm5.32da 425 . . . . 5  C  C  C
128, 11bitr4d 180 . . . 4  C  C
1312eubidv 1905 . . 3  C  C
145, 13mpbid 135 . 2  C  C
15 df-reu 2307 . 2  C  C
1614, 15sylibr 137 1  C  C
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   w3a 884   wceq 1242   wcel 1390  weu 1897  wreu 2302   _Vcvv 2551
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-reu 2307  df-v 2553
This theorem is referenced by:  reuhyp  4170
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