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Theorem euxfrdc 2727
 Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 14-Nov-2004.)
Hypotheses
Ref Expression
euxfrdc.1
euxfrdc.2
euxfrdc.3
Assertion
Ref Expression
euxfrdc DECID
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem euxfrdc
StepHypRef Expression
1 euxfrdc.2 . . . . . 6
2 euex 1930 . . . . . 6
31, 2ax-mp 7 . . . . 5
43biantrur 287 . . . 4
5 19.41v 1782 . . . 4
6 euxfrdc.3 . . . . . 6
76pm5.32i 427 . . . . 5
87exbii 1496 . . . 4
94, 5, 83bitr2i 197 . . 3
109eubii 1909 . 2
11 euxfrdc.1 . . 3
121eumoi 1933 . . 3
1311, 12euxfr2dc 2726 . 2 DECID
1410, 13syl5bb 181 1 DECID
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  DECID wdc 742   wceq 1243  wex 1381   wcel 1393  weu 1900  cvv 2557 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-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-dc 743  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559 This theorem is referenced by: (None)
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