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Theorem eusv2 4215
 Description: Two ways to express single-valuedness of a class expression . (Contributed by NM, 15-Oct-2010.) (Proof shortened by Mario Carneiro, 18-Nov-2016.)
Hypothesis
Ref Expression
eusv2.1
Assertion
Ref Expression
eusv2
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eusv2
StepHypRef Expression
1 eusv2.1 . . 3
21eusv2nf 4214 . 2
3 eusvnfb 4212 . . 3
41, 3mpbiran2 883 . 2
52, 4bitr4i 185 1
 Colors of variables: wff set class Syntax hints:   wb 103  wal 1283   wceq 1285  wex 1422   wcel 1434  weu 1942  wnfc 2207  cvv 2602 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 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-sbc 2817  df-csb 2910  df-un 2978  df-sn 3412  df-pr 3413  df-uni 3610 This theorem is referenced by: (None)
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