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Theorem nfse 4063
 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
nffr.r
nffr.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 4056 . 2 Se
2 nffr.a . . 3
3 nfcv 2175 . . . . . 6
4 nffr.r . . . . . 6
5 nfcv 2175 . . . . . 6
63, 4, 5nfbr 3799 . . . . 5
76, 2nfrabxy 2484 . . . 4
87nfel1 2185 . . 3
92, 8nfralxy 2354 . 2
101, 9nfxfr 1360 1 Se
 Colors of variables: wff set class Syntax hints:  wnf 1346   wcel 1390  wnfc 2162  wral 2300  crab 2304  cvv 2551   class class class wbr 3755   Se wse 4055 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rab 2309  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-se 4056 This theorem is referenced by: (None)
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