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Theorem bj-nfcrii 32551
Description: Remove dependency on ax-ext 2601 (and df-cleq 2614) from nfcrii 2754. (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 2753 . . . 4 (𝑥𝐴 → Ⅎ𝑥 𝑧𝐴)
31, 2ax-mp 5 . . 3 𝑥 𝑧𝐴
43nf5ri 2063 . 2 (𝑧𝐴 → ∀𝑥 𝑧𝐴)
54bj-hblem 32549 1 (𝑦𝐴 → ∀𝑥 𝑦𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  wnf 1705  wcel 1987  wnfc 2748
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clel 2617  df-nfc 2750
This theorem is referenced by:  bj-nfcri  32552
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