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Theorem nfeud 2013
Description: Deduction version of nfeu 2016. (Contributed by NM, 15-Feb-2013.) (Revised by Mario Carneiro, 7-Oct-2016.) (Proof rewritten by Jim Kingdon, 25-May-2018.)
Hypotheses
Ref Expression
nfeud.1  |-  F/ y
ph
nfeud.2  |-  ( ph  ->  F/ x ps )
Assertion
Ref Expression
nfeud  |-  ( ph  ->  F/ x E! y ps )

Proof of Theorem nfeud
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 nfv 1508 . . 3  |-  F/ z ps
21sb8eu 2010 . 2  |-  ( E! y ps  <->  E! z [ z  /  y ] ps )
3 nfv 1508 . . 3  |-  F/ z
ph
4 nfeud.1 . . . 4  |-  F/ y
ph
5 nfeud.2 . . . 4  |-  ( ph  ->  F/ x ps )
64, 5nfsbd 1948 . . 3  |-  ( ph  ->  F/ x [ z  /  y ] ps )
73, 6nfeudv 2012 . 2  |-  ( ph  ->  F/ x E! z [ z  /  y ] ps )
82, 7nfxfrd 1451 1  |-  ( ph  ->  F/ x E! y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1436   [wsb 1735   E!weu 1997
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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2000
This theorem is referenced by:  nfmod  2014  hbeud  2019  nfreudxy  2602
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