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Theorem nfeu1 1954
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 1946 . 2 (∃!𝑥𝜑 ↔ ∃𝑦𝑥(𝜑𝑥 = 𝑦))
2 nfa1 1475 . . 3 𝑥𝑥(𝜑𝑥 = 𝑦)
32nfex 1569 . 2 𝑥𝑦𝑥(𝜑𝑥 = 𝑦)
41, 3nfxfr 1404 1 𝑥∃!𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wb 103  wal 1283  wnf 1390  wex 1422  ∃!weu 1943
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-eu 1946
This theorem is referenced by:  nfmo1  1955  moaneu  2019  nfreu1  2531  eusv2i  4241  eusv2nf  4242  iota2  4960  sniota  4961  fv3  5273  tz6.12c  5279  eusvobj1  5578
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