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Theorem eqeu 2771
 Description: A condition which implies existential uniqueness. (Contributed by Jeff Hankins, 8-Sep-2009.)
Hypothesis
Ref Expression
eqeu.1
Assertion
Ref Expression
eqeu
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem eqeu
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeu.1 . . . . 5
21spcegv 2695 . . . 4
32imp 122 . . 3
433adant3 959 . 2
5 eqeq2 2092 . . . . . . 7
65imbi2d 228 . . . . . 6
76albidv 1747 . . . . 5
87spcegv 2695 . . . 4
98imp 122 . . 3
1093adant2 958 . 2
11 nfv 1462 . . 3
1211eu3 1989 . 2
134, 10, 12sylanbrc 408 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   w3a 920  wal 1283   wceq 1285  wex 1422   wcel 1434  weu 1943 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-eu 1946  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612 This theorem is referenced by: (None)
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