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Theorem dvelimnf 2017
 Description: Version of dvelim 2016 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 1619 . 2 zψ
3 dvelimnf.2 . 2 (z = y → (φψ))
41, 2, 3dvelimf 1997 1 x x = y → Ⅎxψ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176  ∀wal 1540  Ⅎwnf 1544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  nfrab  2792
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