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Theorem nfnfc1 2197
Description: 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 2183 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 nfnf1 1452 . . 3 𝑥𝑥 𝑦𝐴
32nfal 1484 . 2 𝑥𝑦𝑥 𝑦𝐴
41, 3nfxfr 1379 1 𝑥𝑥𝐴
Colors of variables: wff set class
Syntax hints:  wal 1257  wnf 1365  wcel 1409  wnfc 2181
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-nfc 2183
This theorem is referenced by:  vtoclgft  2621  sbcralt  2861  sbcrext  2862  csbiebt  2913  nfopd  3593  nfimad  4704  nffvd  5214
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