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Theorem nfeu1 1986
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 1978 . 2 (∃!𝑥𝜑 ↔ ∃𝑦𝑥(𝜑𝑥 = 𝑦))
2 nfa1 1504 . . 3 𝑥𝑥(𝜑𝑥 = 𝑦)
32nfex 1599 . 2 𝑥𝑦𝑥(𝜑𝑥 = 𝑦)
41, 3nfxfr 1433 1 𝑥∃!𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wb 104  wal 1312  wnf 1419  wex 1451  ∃!weu 1975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-eu 1978
This theorem is referenced by:  nfmo1  1987  moaneu  2051  nfreu1  2577  eusv2i  4344  eusv2nf  4345  iota2  5082  sniota  5083  fv3  5410  tz6.12c  5417  eusvobj1  5727
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