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Theorem nfnfc1 2335
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 2321 . 2  |-  ( F/_ x A  <->  A. y F/ x  y  e.  A )
2 nfnf1 1555 . . 3  |-  F/ x F/ x  y  e.  A
32nfal 1587 . 2  |-  F/ x A. y F/ x  y  e.  A
41, 3nfxfr 1485 1  |-  F/ x F/_ x A
Colors of variables: wff set class
Syntax hints:   A.wal 1362   F/wnf 1471    e. wcel 2160   F/_wnfc 2319
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-nfc 2321
This theorem is referenced by:  vtoclgft  2802  sbcralt  3054  sbcrext  3055  csbiebt  3111  nfopd  3810  nfimad  4997  nffvd  5546
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