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Theorem nfnfc1 2588
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 2573 . 2  |-  ( F/_ x A  <->  A. y F/ x  y  e.  A )
2 nfnf1 1955 . . 3  |-  F/ x F/ x  y  e.  A
32nfal 2004 . 2  |-  F/ x A. y F/ x  y  e.  A
41, 3nfxfr 1693 1  |-  F/ x F/_ x A
Colors of variables: wff setvar class
Syntax hints:   A.wal 1436   F/wnf 1664    e. wcel 1869   F/_wnfc 2571
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906
This theorem depends on definitions:  df-bi 189  df-ex 1661  df-nf 1665  df-nfc 2573
This theorem is referenced by:  vtoclgft  3130  sbcralt  3373  sbcrext  3374  csbiebt  3416  nfopd  4202  nfimad  5194  nffvd  5888
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