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Theorem nfnfc1 2977
Description: The setvar 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 2960 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 2149 . . 3 𝑥𝑥 𝑦𝐴
32nfal 2333 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1844 1 𝑥𝑥𝐴
Colors of variables: wff setvar class
Syntax hints:  wal 1526  wnf 1775  wcel 2105  wnfc 2958
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-10 2136  ax-11 2151  ax-12 2167
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-ex 1772  df-nf 1776  df-nfc 2960
This theorem is referenced by:  vtoclgft  3551  vtoclgftOLD  3552  sbcralt  3852  sbcrext  3853  csbiebt  3909  nfopd  4812  nfimad  5931  nffvd  6675  wl-dfrmof  34736  wl-dfrabf  34745  nfded  35983  nfded2  35984  nfunidALT2  35985
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