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Theorem nfnfc 2289
 Description: Hypothesis builder for Ⅎ𝑦𝐴. (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 2271 . 2 (𝑦𝐴 ↔ ∀𝑧𝑦 𝑧𝐴)
2 nfnfc.1 . . . . 5 𝑥𝐴
32nfcri 2276 . . . 4 𝑥 𝑧𝐴
43nfnf 1557 . . 3 𝑥𝑦 𝑧𝐴
54nfal 1556 . 2 𝑥𝑧𝑦 𝑧𝐴
61, 5nfxfr 1451 1 𝑥𝑦𝐴
 Colors of variables: wff set class Syntax hints:  ∀wal 1330  Ⅎwnf 1437   ∈ wcel 1481  Ⅎwnfc 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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-cleq 2133  df-clel 2136  df-nfc 2271 This theorem is referenced by: (None)
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