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Theorem nfrel 4774
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 4696 . 2  |-  ( Rel 
A  <->  A  C_  ( _V 
X.  _V ) )
2 nfrel.1 . . 3  |-  F/_ x A
3 nfcv 2419 . . 3  |-  F/_ x
( _V  X.  _V )
42, 3nfss 3173 . 2  |-  F/ x  A  C_  ( _V  X.  _V )
51, 4nfxfr 1557 1  |-  F/ x Rel  A
Colors of variables: wff set class
Syntax hints:   F/wnf 1531   F/_wnfc 2406   _Vcvv 2788    C_ wss 3152    X. cxp 4687   Rel wrel 4694
This theorem is referenced by:  nffun  5277
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-in 3159  df-ss 3166  df-rel 4696
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