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Theorem nfnfc1 2258
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 2244 . 2  |-  ( F/_ x A  <->  A. y F/ x  y  e.  A )
2 nfnf1 1506 . . 3  |-  F/ x F/ x  y  e.  A
32nfal 1538 . 2  |-  F/ x A. y F/ x  y  e.  A
41, 3nfxfr 1433 1  |-  F/ x F/_ x A
Colors of variables: wff set class
Syntax hints:   A.wal 1312   F/wnf 1419    e. wcel 1463   F/_wnfc 2242
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 1406  ax-7 1407  ax-gen 1408  ax-4 1470  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-nfc 2244
This theorem is referenced by:  vtoclgft  2707  sbcralt  2953  sbcrext  2954  csbiebt  3005  nfopd  3688  nfimad  4848  nffvd  5387
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