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Theorem nfeud 1932
Description: Deduction version of nfeu 1935. (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 1437 . . 3  |-  F/ z ps
21sb8eu 1929 . 2  |-  ( E! y ps  <->  E! z [ z  /  y ] ps )
3 nfv 1437 . . 3  |-  F/ z
ph
4 nfeud.1 . . . 4  |-  F/ y
ph
5 nfeud.2 . . . 4  |-  ( ph  ->  F/ x ps )
64, 5nfsbd 1867 . . 3  |-  ( ph  ->  F/ x [ z  /  y ] ps )
73, 6nfeudv 1931 . 2  |-  ( ph  ->  F/ x E! z [ z  /  y ] ps )
82, 7nfxfrd 1380 1  |-  ( ph  ->  F/ x E! y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1365   [wsb 1661   E!weu 1916
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-eu 1919
This theorem is referenced by:  nfmod  1933  hbeud  1938  nfreudxy  2500
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