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Theorem nfeud 2472
 Description: Deduction version of nfeu 2474. (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 480 . 2 ((𝜑 ∧ ¬ ∀𝑥 𝑥 = 𝑦) → Ⅎ𝑥𝜓)
41, 3nfeud2 2470 1 (𝜑 → Ⅎ𝑥∃!𝑦𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1473  Ⅎwnf 1699  ∃!weu 2458 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462 This theorem is referenced by:  nfeu  2474
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