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Theorem nfrel 4710
Description: Bound-variable hypothesis builder for a relation. (Contributed by NM, 31-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfrel.1  |-  F/_ x A
Assertion
Ref Expression
nfrel  |-  F/ x Rel  A

Proof of Theorem nfrel
StepHypRef Expression
1 df-rel 4632 . 2  |-  ( Rel 
A  <->  A  C_  ( _V 
X.  _V ) )
2 nfrel.1 . . 3  |-  F/_ x A
3 nfcv 2319 . . 3  |-  F/_ x
( _V  X.  _V )
42, 3nfss 3148 . 2  |-  F/ x  A  C_  ( _V  X.  _V )
51, 4nfxfr 1474 1  |-  F/ x Rel  A
Colors of variables: wff set class
Syntax hints:   F/wnf 1460   F/_wnfc 2306   _Vcvv 2737    C_ wss 3129    X. cxp 4623   Rel wrel 4630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-in 3135  df-ss 3142  df-rel 4632
This theorem is referenced by:  nffun  5238
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