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Theorem bj-nfcrii 32045
 Description: Remove dependency on ax-ext 2590 (and df-cleq 2603) from nfcrii 2744. (Contributed by BJ, 6-Oct-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-nfcri.1 𝑥𝐴
Assertion
Ref Expression
bj-nfcrii (𝑦𝐴 → ∀𝑥 𝑦𝐴)
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝐴(𝑥,𝑦)

Proof of Theorem bj-nfcrii
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 bj-nfcri.1 . . . 4 𝑥𝐴
2 nfcr 2743 . . . 4 (𝑥𝐴 → Ⅎ𝑥 𝑧𝐴)
31, 2ax-mp 5 . . 3 𝑥 𝑧𝐴
43nf5ri 2053 . 2 (𝑧𝐴 → ∀𝑥 𝑧𝐴)
54bj-hblem 32043 1 (𝑦𝐴 → ∀𝑥 𝑦𝐴)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1473  Ⅎwnf 1699   ∈ wcel 1977  Ⅎwnfc 2738 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clel 2606  df-nfc 2740 This theorem is referenced by:  bj-nfcri  32046
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