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Theorem nfnfc1 2627
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 2612 . 2  |-  ( F/_ x A  <->  A. y F/ x  y  e.  A )
2 nfnf1 1842 . . 3  |-  F/ x F/ x  y  e.  A
32nfal 1889 . 2  |-  F/ x A. y F/ x  y  e.  A
41, 3nfxfr 1620 1  |-  F/ x F/_ x A
Colors of variables: wff setvar class
Syntax hints:   A.wal 1372   F/wnf 1594    e. wcel 1762   F/_wnfc 2610
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798
This theorem depends on definitions:  df-bi 185  df-ex 1592  df-nf 1595  df-nfc 2612
This theorem is referenced by:  vtoclgft  3156  sbcralt  3407  sbcrextOLD  3408  sbcrext  3409  csbiebt  3450  nfopd  4225  nfimad  5339  nffvd  5868
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