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Theorem nfnfc1 2181
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 2167 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 1436 . . 3 𝑥𝑥 𝑦𝐴
32nfal 1468 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1363 1 𝑥𝑥𝐴
Colors of variables: wff set class
Syntax hints:  wal 1241  wnf 1349  wcel 1393  wnfc 2165
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-4 1400  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-nfc 2167
This theorem is referenced by:  vtoclgft  2604  sbcralt  2834  sbcrext  2835  csbiebt  2886  nfopd  3566  nfimad  4677  nffvd  5187
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