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Theorem eusv1 4373
 Description: Two ways to express single-valuedness of a class expression . (Contributed by NM, 14-Oct-2010.)
Assertion
Ref Expression
eusv1
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eusv1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sp 1488 . . . 4
2 sp 1488 . . . 4
3 eqtr3 2159 . . . 4
41, 2, 3syl2an 287 . . 3
54gen2 1426 . 2
6 eqeq1 2146 . . . 4
76albidv 1796 . . 3
87eu4 2061 . 2
95, 8mpbiran2 925 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1329   wceq 1331  wex 1468  weu 1999 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-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-cleq 2132 This theorem is referenced by:  eusvnfb  4375
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