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Theorem reuhypd 4392
 Description: A theorem useful for eliminating restricted existential uniqueness hypotheses. (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 2697 . . . . 5
31, 2syl 14 . . . 4
4 eueq 2855 . . . 4
53, 4sylib 121 . . 3
6 eleq1 2202 . . . . . . 7
71, 6syl5ibrcom 156 . . . . . 6
87pm4.71rd 391 . . . . 5
9 reuhypd.2 . . . . . . 7
1093expa 1181 . . . . . 6
1110pm5.32da 447 . . . . 5
128, 11bitr4d 190 . . . 4
1312eubidv 2007 . . 3
145, 13mpbid 146 . 2
15 df-reu 2423 . 2
1614, 15sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   w3a 962   wceq 1331   wcel 1480  weu 1999  wreu 2418  cvv 2686 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-reu 2423  df-v 2688 This theorem is referenced by:  reuhyp  4393
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