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Theorem nfeu1 1927
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 1919 . 2 (∃!𝑥𝜑 ↔ ∃𝑦𝑥(𝜑𝑥 = 𝑦))
2 nfa1 1450 . . 3 𝑥𝑥(𝜑𝑥 = 𝑦)
32nfex 1544 . 2 𝑥𝑦𝑥(𝜑𝑥 = 𝑦)
41, 3nfxfr 1379 1 𝑥∃!𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wb 102  wal 1257  wnf 1365  wex 1397  ∃!weu 1916
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-eu 1919
This theorem is referenced by:  nfmo1  1928  moaneu  1992  nfreu1  2498  eusv2i  4214  eusv2nf  4215  iota2  4920  sniota  4921  fv3  5224  tz6.12c  5230  eusvobj1  5526
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