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Theorem nfnfc1 2577
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 2563 . 2  |-  ( F/_ x A  <->  A. y F/ x  y  e.  A )
2 nfnf1 1809 . . 3  |-  F/ x F/ x  y  e.  A
32nfal 1865 . 2  |-  F/ x A. y F/ x  y  e.  A
41, 3nfxfr 1580 1  |-  F/ x F/_ x A
Colors of variables: wff set class
Syntax hints:   A.wal 1550   F/wnf 1554    e. wcel 1726   F/_wnfc 2561
This theorem is referenced by:  vtoclgft  3004  sbcralt  3235  sbcrext  3236  csbiebt  3289  nfopd  4003  nfimad  5214  nffvd  5739
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555  df-nfc 2563
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