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Theorem nfraldxy 2356
 Description: Not-free for restricted universal quantification where and are distinct. See nfraldya 2358 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 2311 . 2
2 nfraldxy.2 . . 3
3 nfcv 2178 . . . . . 6
43a1i 9 . . . . 5
5 nfraldxy.3 . . . . 5
64, 5nfeld 2193 . . . 4
7 nfraldxy.4 . . . 4
86, 7nfimd 1477 . . 3
92, 8nfald 1643 . 2
101, 9nfxfrd 1364 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1241  wnf 1349   wcel 1393  wnfc 2165  wral 2306 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-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311 This theorem is referenced by:  nfraldya  2358  nfralxy  2360
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