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Theorem eusv1 4717
 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 1763 . . . 4
2 sp 1763 . . . 4
3 eqtr3 2455 . . . 4
41, 2, 3syl2an 464 . . 3
54gen2 1556 . 2
6 eqeq1 2442 . . . 4
76albidv 1635 . . 3
87eu4 2320 . 2
95, 8mpbiran2 886 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550   wceq 1652  weu 2281 This theorem is referenced by:  eusvnfb  4719 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-cleq 2429
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