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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  F/_ R
nffr.a  F/_
Assertion
Ref Expression
nfse  F/  R Se

Proof of Theorem nfse
Dummy variables  a  b are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-se 4056 . 2  R Se  b  { a  |  a R b }  _V
2 nffr.a . . 3  F/_
3 nfcv 2175 . . . . . 6  F/_ a
4 nffr.r . . . . . 6  F/_ R
5 nfcv 2175 . . . . . 6  F/_ b
63, 4, 5nfbr 3799 . . . . 5  F/  a R b
76, 2nfrabxy 2484 . . . 4  F/_ { a  |  a R b }
87nfel1 2185 . . 3  F/ { a  |  a R b }  _V
92, 8nfralxy 2354 . 2  F/ b  { a  |  a R b }  _V
101, 9nfxfr 1360 1  F/  R Se
Colors of variables: wff set class
Syntax hints:   F/wnf 1346   wcel 1390   F/_wnfc 2162  wral 2300   {crab 2304   _Vcvv 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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