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Theorem nfnfc1 2764
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 2750 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 2028 . . 3 𝑥𝑥 𝑦𝐴
32nfal 2150 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1776 1 𝑥𝑥𝐴
Colors of variables: wff setvar class
Syntax hints:  wal 1478  wnf 1705  wcel 1987  wnfc 2748
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-11 2031  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707  df-nfc 2750
This theorem is referenced by:  vtoclgft  3240  vtoclgftOLD  3241  sbcralt  3492  sbcrext  3493  sbcrextOLD  3494  csbiebt  3534  nfopd  4387  nfimad  5434  nffvd  6157  nfded  33731  nfded2  33732  nfunidALT2  33733
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