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Theorem nfres 5150
Description: Bound-variable hypothesis builder for restriction. (Contributed by NM, 15-Sep-2003.) (Revised by David Abernethy, 19-Jun-2012.)
Hypotheses
Ref Expression
nfres.1  |-  F/_ x A
nfres.2  |-  F/_ x B
Assertion
Ref Expression
nfres  |-  F/_ x
( A  |`  B )

Proof of Theorem nfres
StepHypRef Expression
1 df-res 4892 . 2  |-  ( A  |`  B )  =  ( A  i^i  ( B  X.  _V ) )
2 nfres.1 . . 3  |-  F/_ x A
3 nfres.2 . . . 4  |-  F/_ x B
4 nfcv 2574 . . . 4  |-  F/_ x _V
53, 4nfxp 4906 . . 3  |-  F/_ x
( B  X.  _V )
62, 5nfin 3549 . 2  |-  F/_ x
( A  i^i  ( B  X.  _V ) )
71, 6nfcxfr 2571 1  |-  F/_ x
( A  |`  B )
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2561   _Vcvv 2958    i^i cin 3321    X. cxp 4878    |` cres 4882
This theorem is referenced by:  nfima  5213  frsucmpt  6697  frsucmptn  6698  nfoi  7485  prdsdsf  18399  prdsxmet  18401  limciun  19783  trpredlem1  25507  trpredrec  25518  nfwrecs  25535  stoweidlem28  27755  nfdfat  27972  bnj1446  29476  bnj1447  29477  bnj1448  29478  bnj1466  29484  bnj1467  29485  bnj1519  29496  bnj1520  29497  bnj1529  29501
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-in 3329  df-opab 4269  df-xp 4886  df-res 4892
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