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Theorem nfrel 4937
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 4858 . 2  |-  ( Rel 
A  <->  A  C_  ( _V 
X.  _V ) )
2 nfrel.1 . . 3  |-  F/_ x A
3 nfcv 2585 . . 3  |-  F/_ x
( _V  X.  _V )
42, 3nfss 3458 . 2  |-  F/ x  A  C_  ( _V  X.  _V )
51, 4nfxfr 1693 1  |-  F/ x Rel  A
Colors of variables: wff setvar class
Syntax hints:   F/wnf 1664   F/_wnfc 2571   _Vcvv 3082    C_ wss 3437    X. cxp 4849   Rel wrel 4856
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ral 2781  df-in 3444  df-ss 3451  df-rel 4858
This theorem is referenced by:  nffun  5621
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