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Theorem nfrel 4965
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 4888 . 2  |-  ( Rel 
A  <->  A  C_  ( _V 
X.  _V ) )
2 nfrel.1 . . 3  |-  F/_ x A
3 nfcv 2574 . . 3  |-  F/_ x
( _V  X.  _V )
42, 3nfss 3343 . 2  |-  F/ x  A  C_  ( _V  X.  _V )
51, 4nfxfr 1580 1  |-  F/ x Rel  A
Colors of variables: wff set class
Syntax hints:   F/wnf 1554   F/_wnfc 2561   _Vcvv 2958    C_ wss 3322    X. cxp 4879   Rel wrel 4886
This theorem is referenced by:  nffun  5479
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-ral 2712  df-in 3329  df-ss 3336  df-rel 4888
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