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Theorem bj-dvelimv 32961
Description: A version of dvelim 2368 using the "non-free" idiom. (Contributed by BJ, 20-Oct-2021.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-dvelimv.nf 𝑥𝜓
bj-dvelimv.is (𝑧 = 𝑦 → (𝜓𝜑))
Assertion
Ref Expression
bj-dvelimv (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜑)
Distinct variable groups:   𝑥,𝑧   𝑦,𝑧   𝜑,𝑧
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑥,𝑦,𝑧)

Proof of Theorem bj-dvelimv
StepHypRef Expression
1 nfv 1883 . . 3 𝑥
2 bj-dvelimv.nf . . . 4 𝑥𝜓
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜓)
4 bj-dvelimv.is . . 3 (𝑧 = 𝑦 → (𝜓𝜑))
51, 3, 4bj-dvelimdv1 32960 . 2 (⊤ → (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜑))
65trud 1533 1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wal 1521  wtru 1524  wnf 1748
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750
This theorem is referenced by:  bj-nfeel2  32962
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