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Theorem nfcii 2273
Description: Deduce that a class 𝐴 does not have 𝑥 free in it. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfcii.1 (𝑦𝐴 → ∀𝑥 𝑦𝐴)
Assertion
Ref Expression
nfcii 𝑥𝐴
Distinct variable groups:   𝑥,𝑦   𝑦,𝐴
Allowed substitution hint:   𝐴(𝑥)

Proof of Theorem nfcii
StepHypRef Expression
1 nfcii.1 . . 3 (𝑦𝐴 → ∀𝑥 𝑦𝐴)
21nfi 1439 . 2 𝑥 𝑦𝐴
32nfci 2272 1 𝑥𝐴
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1330  wcel 1481  wnfc 2269
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1426
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-nfc 2271
This theorem is referenced by: (None)
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