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

Theorem nfeu1 1953
Description: Bound-variable hypothesis builder for uniqueness. (Contributed by NM, 9-Jul-1994.) (Revised by Mario Carneiro, 7-Oct-2016.)
Assertion
Ref Expression
nfeu1  |-  F/ x E! x ph

Proof of Theorem nfeu1
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 df-eu 1945 . 2  |-  ( E! x ph  <->  E. y A. x ( ph  <->  x  =  y ) )
2 nfa1 1475 . . 3  |-  F/ x A. x ( ph  <->  x  =  y )
32nfex 1569 . 2  |-  F/ x E. y A. x (
ph 
<->  x  =  y )
41, 3nfxfr 1404 1  |-  F/ x E! x ph
Colors of variables: wff set class
Syntax hints:    <-> wb 103   A.wal 1283   F/wnf 1390   E.wex 1422   E!weu 1942
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 1945
This theorem is referenced by:  nfmo1  1954  moaneu  2018  nfreu1  2526  eusv2i  4213  eusv2nf  4214  iota2  4923  sniota  4924  fv3  5229  tz6.12c  5235  eusvobj1  5530
  Copyright terms: Public domain W3C validator