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Theorem nfrel 4929
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 4852 . 2  |-  ( Rel 
A  <->  A  C_  ( _V 
X.  _V ) )
2 nfrel.1 . . 3  |-  F/_ x A
3 nfcv 2548 . . 3  |-  F/_ x
( _V  X.  _V )
42, 3nfss 3309 . 2  |-  F/ x  A  C_  ( _V  X.  _V )
51, 4nfxfr 1576 1  |-  F/ x Rel  A
Colors of variables: wff set class
Syntax hints:   F/wnf 1550   F/_wnfc 2535   _Vcvv 2924    C_ wss 3288    X. cxp 4843   Rel wrel 4850
This theorem is referenced by:  nffun  5443
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ral 2679  df-in 3295  df-ss 3302  df-rel 4852
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