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Theorem nfcrii 2899
Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.) Avoid ax-10 2140, ax-11 2156. (Revised by GG, 23-May-2024.)
Hypothesis
Ref Expression
nfcrii.1 𝑥𝐴
Assertion
Ref Expression
nfcrii (𝑦𝐴 → ∀𝑥 𝑦𝐴)
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝐴(𝑥,𝑦)

Proof of Theorem nfcrii
StepHypRef Expression
1 nfcrii.1 . . 3 𝑥𝐴
21nfcri 2896 . 2 𝑥 𝑦𝐴
32nf5ri 2194 1 (𝑦𝐴 → ∀𝑥 𝑦𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1537  wcel 2107  wnfc 2889
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-12 2176
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-nf 1783  df-clel 2815  df-nfc 2891
This theorem is referenced by:  bnj1230  34817  bnj1000  34956  bnj1204  35027  bnj1307  35038  bnj1311  35039  bnj1398  35049  bnj1466  35068  bnj1467  35069  bnj1523  35086
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