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Theorem nfnfc1 2342
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 2328 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 1558 . . 3 𝑥𝑥 𝑦𝐴
32nfal 1590 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1488 1 𝑥𝑥𝐴
Colors of variables: wff set class
Syntax hints:  wal 1362  wnf 1474  wcel 2167  wnfc 2326
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 1461  ax-7 1462  ax-gen 1463  ax-ial 1548
This theorem depends on definitions:  df-bi 117  df-nf 1475  df-nfc 2328
This theorem is referenced by:  vtoclgft  2814  sbcralt  3066  sbcrext  3067  csbiebt  3124  nfopd  3825  nfimad  5018  nffvd  5570
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