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Theorem nfnfc1 2435
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 2421 . 2  |-  ( F/_ x A  <->  A. y F/ x  y  e.  A )
2 nfnf1 1769 . . 3  |-  F/ x F/ x  y  e.  A
32nfal 1778 . 2  |-  F/ x A. y F/ x  y  e.  A
41, 3nfxfr 1560 1  |-  F/ x F/_ x A
Colors of variables: wff set class
Syntax hints:   A.wal 1530   F/wnf 1534    e. wcel 1696   F/_wnfc 2419
This theorem is referenced by:  vtoclgft  2847  sbcralt  3076  sbcrext  3077  csbiebt  3130  nfopd  3829  nfimad  5037  nffvd  5550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-nf 1535  df-nfc 2421
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