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Theorem nfeu1 1911
 Description: Bound-variable hypothesis builder for uniqueness. (Contributed by NM, 9-Jul-1994.) (Revised by Mario Carneiro, 7-Oct-2016.)
Assertion
Ref Expression
nfeu1 𝑥∃!𝑥𝜑

Proof of Theorem nfeu1
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-eu 1903 . 2 (∃!𝑥𝜑 ↔ ∃𝑦𝑥(𝜑𝑥 = 𝑦))
2 nfa1 1434 . . 3 𝑥𝑥(𝜑𝑥 = 𝑦)
32nfex 1528 . 2 𝑥𝑦𝑥(𝜑𝑥 = 𝑦)
41, 3nfxfr 1363 1 𝑥∃!𝑥𝜑
 Colors of variables: wff set class Syntax hints:   ↔ wb 98  ∀wal 1241  Ⅎwnf 1349  ∃wex 1381  ∃!weu 1900 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-eu 1903 This theorem is referenced by:  nfmo1  1912  moaneu  1976  nfreu1  2481  eusv2i  4187  eusv2nf  4188  iota2  4893  sniota  4894  fv3  5197  tz6.12c  5203  eusvobj1  5499
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