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Theorem nfnfc1 2908
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 2892 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 2154 . . 3 𝑥𝑥 𝑦𝐴
32nfal 2323 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1853 1 𝑥𝑥𝐴
Colors of variables: wff setvar class
Syntax hints:  wal 1538  wnf 1783  wcel 2108  wnfc 2890
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-10 2141  ax-11 2157  ax-12 2177
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-ex 1780  df-nf 1784  df-nfc 2892
This theorem is referenced by:  cbvexeqsetf  3495  sbcralt  3872  sbcrext  3873  csbiebt  3928  nfopd  4890  nfimad  6087  nffvd  6918  wl-issetft  37583  nfded  38968  nfded2  38969  nfunidALT2  38970
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