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Theorem nfnfc1 2238
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 2224 . 2  |-  ( F/_ x A  <->  A. y F/ x  y  e.  A )
2 nfnf1 1488 . . 3  |-  F/ x F/ x  y  e.  A
32nfal 1520 . 2  |-  F/ x A. y F/ x  y  e.  A
41, 3nfxfr 1415 1  |-  F/ x F/_ x A
Colors of variables: wff set class
Syntax hints:   A.wal 1294   F/wnf 1401    e. wcel 1445   F/_wnfc 2222
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-7 1389  ax-gen 1390  ax-4 1452  ax-ial 1479
This theorem depends on definitions:  df-bi 116  df-nf 1402  df-nfc 2224
This theorem is referenced by:  vtoclgft  2683  sbcralt  2929  sbcrext  2930  csbiebt  2981  nfopd  3661  nfimad  4816  nffvd  5352
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