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Theorem eusvnf 4374
 Description: Even if is free in , it is effectively bound when is single-valued. (Contributed by NM, 14-Oct-2010.) (Revised by Mario Carneiro, 14-Oct-2016.)
Assertion
Ref Expression
eusvnf
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eusvnf
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 euex 2029 . 2
2 vex 2689 . . . . . . 7
3 nfcv 2281 . . . . . . . 8
4 nfcsb1v 3035 . . . . . . . . 9
54nfeq2 2293 . . . . . . . 8
6 csbeq1a 3012 . . . . . . . . 9
76eqeq2d 2151 . . . . . . . 8
83, 5, 7spcgf 2768 . . . . . . 7
92, 8ax-mp 5 . . . . . 6
10 vex 2689 . . . . . . 7
11 nfcv 2281 . . . . . . . 8
12 nfcsb1v 3035 . . . . . . . . 9
1312nfeq2 2293 . . . . . . . 8
14 csbeq1a 3012 . . . . . . . . 9
1514eqeq2d 2151 . . . . . . . 8
1611, 13, 15spcgf 2768 . . . . . . 7
1710, 16ax-mp 5 . . . . . 6
189, 17eqtr3d 2174 . . . . 5
1918alrimivv 1847 . . . 4
20 sbnfc2 3060 . . . 4
2119, 20sylibr 133 . . 3
2221exlimiv 1577 . 2
231, 22syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1329   wceq 1331  wex 1468   wcel 1480  weu 1999  wnfc 2268  cvv 2686  csb 3003 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-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sbc 2910  df-csb 3004 This theorem is referenced by:  eusvnfb  4375  eusv2i  4376
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