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Theorem nfnfc1 2919
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 2905 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 2190 . . 3 𝑥𝑥 𝑦𝐴
32nfal 2320 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1932 1 𝑥𝑥𝐴
Colors of variables: wff setvar class
Syntax hints:  wal 1632  wnf 1859  wcel 2148  wnfc 2903
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1873  ax-4 1888  ax-5 1994  ax-6 2060  ax-7 2096  ax-10 2177  ax-11 2193  ax-12 2206
This theorem depends on definitions:  df-bi 198  df-an 384  df-or 864  df-ex 1856  df-nf 1861  df-nfc 2905
This theorem is referenced by:  vtoclgft  3411  sbcralt  3666  sbcrext  3667  csbiebt  3708  nfopd  4567  nfimad  5626  nffvd  6358  nfded  34791  nfded2  34792  nfunidALT2  34793
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