Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfeu1 GIF version

Theorem nfeu1 2017
 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 2009 . 2 (∃!𝑥𝜑 ↔ ∃𝑦𝑥(𝜑𝑥 = 𝑦))
2 nfa1 1521 . . 3 𝑥𝑥(𝜑𝑥 = 𝑦)
32nfex 1617 . 2 𝑥𝑦𝑥(𝜑𝑥 = 𝑦)
41, 3nfxfr 1454 1 𝑥∃!𝑥𝜑
 Colors of variables: wff set class Syntax hints:   ↔ wb 104  ∀wal 1333  Ⅎwnf 1440  ∃wex 1472  ∃!weu 2006 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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-eu 2009 This theorem is referenced by:  nfmo1  2018  moaneu  2082  nfreu1  2628  eusv2i  4414  eusv2nf  4415  iota2  5160  sniota  5161  fv3  5490  tz6.12c  5497  eusvobj1  5808
 Copyright terms: Public domain W3C validator