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Theorem nfnfc1 2906
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 2890 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 2152 . . 3 𝑥𝑥 𝑦𝐴
32nfal 2322 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1850 1 𝑥𝑥𝐴
Colors of variables: wff setvar class
Syntax hints:  wal 1535  wnf 1780  wcel 2106  wnfc 2888
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-10 2139  ax-11 2155  ax-12 2175
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1777  df-nf 1781  df-nfc 2890
This theorem is referenced by:  cbvexeqsetf  3493  sbcralt  3881  sbcrext  3882  csbiebt  3938  nfopd  4895  nfimad  6089  nffvd  6919  wl-issetft  37563  nfded  38949  nfded2  38950  nfunidALT2  38951
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