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Theorem bj-nfnfc 33159
Description: Remove dependency on ax-ext 2740 (and df-cleq 2753) from nfnfc 2912. (Contributed by BJ, 6-Oct-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-nfnfc.1 𝑥𝐴
Assertion
Ref Expression
bj-nfnfc 𝑥𝑦𝐴

Proof of Theorem bj-nfnfc
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2891 . 2 (𝑦𝐴 ↔ ∀𝑧𝑦 𝑧𝐴)
2 bj-nfnfc.1 . . . . 5 𝑥𝐴
32bj-nfcri 33158 . . . 4 𝑥 𝑧𝐴
43nfnf 2305 . . 3 𝑥𝑦 𝑧𝐴
54nfal 2300 . 2 𝑥𝑧𝑦 𝑧𝐴
61, 5nfxfr 1928 1 𝑥𝑦𝐴
Colors of variables: wff setvar class
Syntax hints:  wal 1630  wnf 1857  wcel 2139  wnfc 2889
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clel 2756  df-nfc 2891
This theorem is referenced by: (None)
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