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Theorem nfcrii 2887
Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.) Avoid ax-10 2129, ax-11 2146. (Revised by Gino Giotto, 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 2882 . 2 𝑥 𝑦𝐴
32nf5ri 2180 1 (𝑦𝐴 → ∀𝑥 𝑦𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1531  wcel 2098  wnfc 2875
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-12 2163
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774  df-nf 1778  df-clel 2802  df-nfc 2877
This theorem is referenced by:  nfcriOLDOLDOLD  2889  bnj1230  34302  bnj1000  34441  bnj1204  34512  bnj1307  34523  bnj1311  34524  bnj1398  34534  bnj1466  34553  bnj1467  34554  bnj1523  34571
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