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Theorem nfnfc1 2285
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 2271 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 1524 . . 3 𝑥𝑥 𝑦𝐴
32nfal 1556 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1451 1 𝑥𝑥𝐴
Colors of variables: wff set class
Syntax hints:  wal 1330  wnf 1437  wcel 1481  wnfc 2269
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-4 1488  ax-ial 1515
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-nfc 2271
This theorem is referenced by:  vtoclgft  2739  sbcralt  2988  sbcrext  2989  csbiebt  3042  nfopd  3728  nfimad  4896  nffvd  5439
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