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Theorem nfraldxy 2471
 Description: Not-free for restricted universal quantification where and are distinct. See nfraldya 2473 for a version with and distinct instead. (Contributed by Jim Kingdon, 29-May-2018.)
Hypotheses
Ref Expression
nfraldxy.2
nfraldxy.3
nfraldxy.4
Assertion
Ref Expression
nfraldxy
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem nfraldxy
StepHypRef Expression
1 df-ral 2422 . 2
2 nfraldxy.2 . . 3
3 nfcv 2282 . . . . . 6
43a1i 9 . . . . 5
5 nfraldxy.3 . . . . 5
64, 5nfeld 2298 . . . 4
7 nfraldxy.4 . . . 4
86, 7nfimd 1565 . . 3
92, 8nfald 1734 . 2
101, 9nfxfrd 1452 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1330  wnf 1437   wcel 1481  wnfc 2269  wral 2417 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-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422 This theorem is referenced by:  nfraldya  2473  nfralxy  2475  strcollnft  13373
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