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Theorem nfeu1 1959
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 1951 . 2 (∃!𝑥𝜑 ↔ ∃𝑦𝑥(𝜑𝑥 = 𝑦))
2 nfa1 1479 . . 3 𝑥𝑥(𝜑𝑥 = 𝑦)
32nfex 1573 . 2 𝑥𝑦𝑥(𝜑𝑥 = 𝑦)
41, 3nfxfr 1408 1 𝑥∃!𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wb 103  wal 1287  wnf 1394  wex 1426  ∃!weu 1948
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 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-eu 1951
This theorem is referenced by:  nfmo1  1960  moaneu  2024  nfreu1  2538  eusv2i  4268  eusv2nf  4269  iota2  4993  sniota  4994  fv3  5312  tz6.12c  5318  eusvobj1  5621
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