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Theorem bj-nfcjust 33148
Description: Remove dependency on ax-ext 2732 (and df-cleq 2745 and ax-13 2383) from nfcjust 2882. (Contributed by BJ, 24-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-nfcjust (∀𝑦𝑥 𝑦𝐴 ↔ ∀𝑧𝑥 𝑧𝐴)
Distinct variable groups:   𝑥,𝑦,𝑧   𝑦,𝐴,𝑧
Allowed substitution hint:   𝐴(𝑥)

Proof of Theorem bj-nfcjust
StepHypRef Expression
1 nfv 1984 . . 3 𝑥 𝑦 = 𝑧
2 eleq1w 2814 . . 3 (𝑦 = 𝑧 → (𝑦𝐴𝑧𝐴))
31, 2nfbidf 2231 . 2 (𝑦 = 𝑧 → (Ⅎ𝑥 𝑦𝐴 ↔ Ⅎ𝑥 𝑧𝐴))
43bj-cbvalvv 33031 1 (∀𝑦𝑥 𝑦𝐴 ↔ ∀𝑧𝑥 𝑧𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wal 1622  wnf 1849  wcel 2131
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1863  ax-4 1878  ax-5 1980  ax-6 2046  ax-7 2082  ax-10 2160  ax-11 2175  ax-12 2188
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1846  df-nf 1851  df-clel 2748
This theorem is referenced by: (None)
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