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Theorem nfeu1 2290
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 2284 . 2  |-  ( E! x ph  <->  E. y A. x ( ph  <->  x  =  y ) )
2 nfa1 1806 . . 3  |-  F/ x A. x ( ph  <->  x  =  y )
32nfex 1865 . 2  |-  F/ x E. y A. x (
ph 
<->  x  =  y )
41, 3nfxfr 1579 1  |-  F/ x E! x ph
Colors of variables: wff set class
Syntax hints:    <-> wb 177   A.wal 1549   E.wex 1550   F/wnf 1553   E!weu 2280
This theorem is referenced by:  nfmo1  2291  moaneu  2339  eupicka  2344  2eu8  2367  exists2  2370  nfreu1  2870  eusv2i  4712  eusv2nf  4713  reusv2lem3  4718  iota2  5436  sniota  5437  fv3  5736  tz6.12c  5742  opiota  6527  eusvobj1  6575  dfac5lem5  7998  pm14.24  27564  eu2ndop1stv  27911  bnj1366  29102  bnj849  29197
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-ex 1551  df-nf 1554  df-eu 2284
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