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Theorem nfnfc1 2339
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 2325 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 1555 . . 3 𝑥𝑥 𝑦𝐴
32nfal 1587 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1485 1 𝑥𝑥𝐴
Colors of variables: wff set class
Syntax hints:  wal 1362  wnf 1471  wcel 2164  wnfc 2323
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-nfc 2325
This theorem is referenced by:  vtoclgft  2810  sbcralt  3062  sbcrext  3063  csbiebt  3120  nfopd  3821  nfimad  5014  nffvd  5566
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