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Theorem nfcii 2935
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)
21nf5i 2115 . 2 𝑥 𝑦𝐴
32nfci 2934 1 𝑥𝐴
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1518  wcel 2079  wnfc 2931
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1775  ax-4 1789  ax-10 2110
This theorem depends on definitions:  df-bi 208  df-ex 1760  df-nf 1764  df-nfc 2933
This theorem is referenced by:  bnj1316  31665  bnj1385  31677  bnj1400  31680  bnj1468  31690  bnj1534  31697  bnj1542  31701  bnj1228  31853  bnj1307  31865  bnj1448  31889  bnj1466  31895  bnj1463  31897  bnj1491  31899  bnj1312  31900  bnj1498  31903  bnj1520  31908  bnj1525  31911  bnj1529  31912  bnj1523  31913
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