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Theorem nfse 4078
 Description: Bound-variable hypothesis builder for set-like relations. (Contributed by Mario Carneiro, 24-Jun-2015.) (Revised by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nfse.r
nfse.a
Assertion
Ref Expression
nfse Se

Proof of Theorem nfse
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-se 4070 . 2 Se
2 nfse.a . . 3
3 nfcv 2178 . . . . . 6
4 nfse.r . . . . . 6
5 nfcv 2178 . . . . . 6
63, 4, 5nfbr 3808 . . . . 5
76, 2nfrabxy 2490 . . . 4
87nfel1 2188 . . 3
92, 8nfralxy 2360 . 2
101, 9nfxfr 1363 1 Se
 Colors of variables: wff set class Syntax hints:  wnf 1349   wcel 1393  wnfc 2165  wral 2306  crab 2310  cvv 2557   class class class wbr 3764   Se wse 4066 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-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rab 2315  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-se 4070 This theorem is referenced by: (None)
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