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Theorem nfnfc1 2226
Description: 𝑥 is bound in 𝑥𝐴. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfnfc1 𝑥𝑥𝐴

Proof of Theorem nfnfc1
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2212 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 1477 . . 3 𝑥𝑥 𝑦𝐴
32nfal 1509 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1404 1 𝑥𝑥𝐴
Colors of variables: wff set class
Syntax hints:  wal 1283  wnf 1390  wcel 1434  wnfc 2210
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-nfc 2212
This theorem is referenced by:  vtoclgft  2660  sbcralt  2901  sbcrext  2902  csbiebt  2953  nfopd  3613  nfimad  4738  nffvd  5262
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