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Theorem nfeud 2218
 Description: Deduction version of nfeu 2220. (Contributed by NM, 15-Feb-2013.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypotheses
Ref Expression
nfeud.1 yφ
nfeud.2 (φ → Ⅎxψ)
Assertion
Ref Expression
nfeud (φ → Ⅎx∃!yψ)

Proof of Theorem nfeud
StepHypRef Expression
1 nfeud.1 . 2 yφ
2 nfeud.2 . . 3 (φ → Ⅎxψ)
32adantr 451 . 2 ((φ ¬ x x = y) → Ⅎxψ)
41, 3nfeud2 2216 1 (φ → Ⅎx∃!yψ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540  Ⅎwnf 1544   = wceq 1642  ∃!weu 2204 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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  df-eu 2208 This theorem is referenced by:  nfeu  2220
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