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Theorem dvelimnf 2370
Description: Version of dvelim 2368 using "not free" notation. (Contributed by Mario Carneiro, 9-Oct-2016.)
Hypotheses
Ref Expression
dvelimnf.1 𝑥𝜑
dvelimnf.2 (𝑧 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
dvelimnf (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜓)
Distinct variable group:   𝜓,𝑧
Allowed substitution hints:   𝜑(𝑥,𝑦,𝑧)   𝜓(𝑥,𝑦)

Proof of Theorem dvelimnf
StepHypRef Expression
1 dvelimnf.1 . 2 𝑥𝜑
2 nfv 1883 . 2 𝑧𝜓
3 dvelimnf.2 . 2 (𝑧 = 𝑦 → (𝜑𝜓))
41, 2, 3dvelimf 2365 1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wal 1521  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:  nfrab  3153
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