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Theorem nfnfc1 2197
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 2183 . 2  |-  ( F/_ x A  <->  A. y F/ x  y  e.  A )
2 nfnf1 1452 . . 3  |-  F/ x F/ x  y  e.  A
32nfal 1484 . 2  |-  F/ x A. y F/ x  y  e.  A
41, 3nfxfr 1379 1  |-  F/ x F/_ x A
Colors of variables: wff set class
Syntax hints:   A.wal 1257   F/wnf 1365    e. wcel 1409   F/_wnfc 2181
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-nfc 2183
This theorem is referenced by:  vtoclgft  2621  sbcralt  2862  sbcrext  2863  csbiebt  2914  nfopd  3594  nfimad  4705  nffvd  5215
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