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Theorem nfnfc 2926
Description: Hypothesis builder for 𝑦𝐴. (Contributed by Mario Carneiro, 11-Aug-2016.) Remove dependency on ax-13 2411. (Revised by Wolf Lammen, 10-Dec-2019.)
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 2905 . 2 (𝑦𝐴 ↔ ∀𝑧𝑦 𝑧𝐴)
2 nfnfc.1 . . . . 5 𝑥𝐴
3 nfcr 2908 . . . . 5 (𝑥𝐴 → Ⅎ𝑥 𝑧𝐴)
42, 3ax-mp 5 . . . 4 𝑥 𝑧𝐴
54nfnf 2325 . . 3 𝑥𝑦 𝑧𝐴
65nfal 2320 . 2 𝑥𝑧𝑦 𝑧𝐴
71, 6nfxfr 1932 1 𝑥𝑦𝐴
Colors of variables: wff setvar class
Syntax hints:  wal 1632  wnf 1859  wcel 2148  wnfc 2903
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1873  ax-4 1888  ax-5 1994  ax-6 2060  ax-7 2096  ax-10 2177  ax-11 2193  ax-12 2206
This theorem depends on definitions:  df-bi 198  df-an 384  df-or 864  df-ex 1856  df-nf 1861  df-nfc 2905
This theorem is referenced by: (None)
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