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Theorem nfnfc1 2422
Description:  x is bound in  F/_ x A. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfnfc1  |-  F/ x F/_ x A

Proof of Theorem nfnfc1
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2408 . 2  |-  ( F/_ x A  <->  A. y F/ x  y  e.  A )
2 nfnf1 1757 . . 3  |-  F/ x F/ x  y  e.  A
32nfal 1766 . 2  |-  F/ x A. y F/ x  y  e.  A
41, 3nfxfr 1557 1  |-  F/ x F/_ x A
Colors of variables: wff set class
Syntax hints:   A.wal 1527   F/wnf 1531    e. wcel 1684   F/_wnfc 2406
This theorem is referenced by:  vtoclgft  2834  sbcralt  3063  sbcrext  3064  csbiebt  3117  nfopd  3813  nfimad  5021  nffvd  5534
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
This theorem depends on definitions:  df-bi 177  df-nf 1532  df-nfc 2408
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