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Theorem dvelimnf 2476
 Description: Version of dvelim 2474 using "not free" notation. Usage of this theorem is discouraged because it depends on ax-13 2391. (Contributed by Mario Carneiro, 9-Oct-2016.) (New usage is discouraged.)
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 1915 . 2 𝑧𝜓
3 dvelimnf.2 . 2 (𝑧 = 𝑦 → (𝜑𝜓))
41, 2, 3dvelimf 2471 1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 209  ∀wal 1536  Ⅎwnf 1785 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2145  ax-11 2161  ax-12 2178  ax-13 2391 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786 This theorem is referenced by:  nfcvf  3005  nfrab  3367
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