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Theorem nfreudxy 2483
 Description: Not-free deduction for restricted uniqueness. This is a version where and are distinct. (Contributed by Jim Kingdon, 6-Jun-2018.)
Hypotheses
Ref Expression
nfreudxy.1
nfreudxy.2
nfreudxy.3
Assertion
Ref Expression
nfreudxy
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem nfreudxy
StepHypRef Expression
1 nfreudxy.1 . . 3
2 nfcv 2178 . . . . . 6
32a1i 9 . . . . 5
4 nfreudxy.2 . . . . 5
53, 4nfeld 2193 . . . 4
6 nfreudxy.3 . . . 4
75, 6nfand 1460 . . 3
81, 7nfeud 1916 . 2
9 df-reu 2313 . . 3
109nfbii 1362 . 2
118, 10sylibr 137 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97  wnf 1349   wcel 1393  weu 1900  wnfc 2165  wreu 2308 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-cleq 2033  df-clel 2036  df-nfc 2167  df-reu 2313 This theorem is referenced by:  nfreuxy  2484
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