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Theorem nfres 4973
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 4717 . 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 2432 . . . 4  |-  F/_ x _V
53, 4nfxp 4731 . . 3  |-  F/_ x
( B  X.  _V )
62, 5nfin 3388 . 2  |-  F/_ x
( A  i^i  ( B  X.  _V ) )
71, 6nfcxfr 2429 1  |-  F/_ x
( A  |`  B )
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2419   _Vcvv 2801    i^i cin 3164    X. cxp 4703    |` cres 4707
This theorem is referenced by:  nfima  5036  frsucmpt  6466  frsucmptn  6467  nfoi  7245  axdclem  8162  prdsdsf  17947  prdsxmet  17949  limciun  19260  trpredlem1  24301  trpredrec  24312  stoweidlem28  27880  nfdfat  28098  bnj1446  29391  bnj1447  29392  bnj1448  29393  bnj1466  29399  bnj1467  29400  bnj1519  29411  bnj1520  29412  bnj1529  29416
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-in 3172  df-opab 4094  df-xp 4711  df-res 4717
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