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Theorem nfnfc1 2796
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 2782 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 2071 . . 3 𝑥𝑥 𝑦𝐴
32nfal 2191 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1819 1 𝑥𝑥𝐴
Colors of variables: wff setvar class
Syntax hints:  wal 1521  wnf 1748  wcel 2030  wnfc 2780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-11 2074  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1745  df-nf 1750  df-nfc 2782
This theorem is referenced by:  vtoclgft  3285  vtoclgftOLD  3286  sbcralt  3543  sbcrext  3544  sbcrextOLD  3545  csbiebt  3586  nfopd  4450  nfimad  5510  nffvd  6238  nfded  34572  nfded2  34573  nfunidALT2  34574
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