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Theorem nfeu1 1956
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 1948 . 2  |-  ( E! x ph  <->  E. y A. x ( ph  <->  x  =  y ) )
2 nfa1 1477 . . 3  |-  F/ x A. x ( ph  <->  x  =  y )
32nfex 1571 . 2  |-  F/ x E. y A. x (
ph 
<->  x  =  y )
41, 3nfxfr 1406 1  |-  F/ x E! x ph
Colors of variables: wff set class
Syntax hints:    <-> wb 103   A.wal 1285   F/wnf 1392   E.wex 1424   E!weu 1945
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-ial 1470
This theorem depends on definitions:  df-bi 115  df-nf 1393  df-eu 1948
This theorem is referenced by:  nfmo1  1957  moaneu  2021  nfreu1  2534  eusv2i  4253  eusv2nf  4254  iota2  4974  sniota  4975  fv3  5293  tz6.12c  5299  eusvobj1  5602
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