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Theorem nfnfc1 2569
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 2554 . 2  |-  ( F/_ x A  <->  A. y F/ x  y  e.  A )
2 nfnf1 1929 . . 3  |-  F/ x F/ x  y  e.  A
32nfal 1977 . 2  |-  F/ x A. y F/ x  y  e.  A
41, 3nfxfr 1668 1  |-  F/ x F/_ x A
Colors of variables: wff setvar class
Syntax hints:   A.wal 1405   F/wnf 1639    e. wcel 1844   F/_wnfc 2552
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880
This theorem depends on definitions:  df-bi 187  df-ex 1636  df-nf 1640  df-nfc 2554
This theorem is referenced by:  vtoclgft  3109  sbcralt  3352  sbcrext  3353  csbiebt  3395  nfopd  4178  nfimad  5168  nffvd  5860
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