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Theorem nfeud 2677
Description: Bound-variable hypothesis builder for the unique existential quantifier. Deduction version of nfeu 2679. Usage of this theorem is discouraged because it depends on ax-13 2390. Use the weaker nfeudw 2676 when possible. (Contributed by NM, 15-Feb-2013.) (Revised by Mario Carneiro, 7-Oct-2016.) (New usage is discouraged.)
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 483 . 2 ((𝜑 ∧ ¬ ∀𝑥 𝑥 = 𝑦) → Ⅎ𝑥𝜓)
41, 3nfeud2 2675 1 (𝜑 → Ⅎ𝑥∃!𝑦𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1535  wnf 1784  ∃!weu 2652
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2145  ax-11 2161  ax-12 2177  ax-13 2390
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-mo 2622  df-eu 2653
This theorem is referenced by:  nfeu  2679
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