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Theorem nfnfc 2265
Description: Hypothesis builder for 𝑦𝐴. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfnfc.1 𝑥𝐴
Assertion
Ref Expression
nfnfc 𝑥𝑦𝐴

Proof of Theorem nfnfc
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2247 . 2 (𝑦𝐴 ↔ ∀𝑧𝑦 𝑧𝐴)
2 nfnfc.1 . . . . 5 𝑥𝐴
32nfcri 2252 . . . 4 𝑥 𝑧𝐴
43nfnf 1541 . . 3 𝑥𝑦 𝑧𝐴
54nfal 1540 . 2 𝑥𝑧𝑦 𝑧𝐴
61, 5nfxfr 1435 1 𝑥𝑦𝐴
Colors of variables: wff set class
Syntax hints:  wal 1314  wnf 1421  wcel 1465  wnfc 2245
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-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-cleq 2110  df-clel 2113  df-nfc 2247
This theorem is referenced by: (None)
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