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Theorem hbeud 1965
Description: Deduction version of hbeu 1964. (Contributed by NM, 15-Feb-2013.) (Proof rewritten by Jim Kingdon, 25-May-2018.)
Hypotheses
Ref Expression
hbeud.1  |-  ( ph  ->  A. x ph )
hbeud.2  |-  ( ph  ->  A. y ph )
hbeud.3  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Assertion
Ref Expression
hbeud  |-  ( ph  ->  ( E! y ps 
->  A. x E! y ps ) )

Proof of Theorem hbeud
StepHypRef Expression
1 hbeud.2 . . . 4  |-  ( ph  ->  A. y ph )
21nfi 1392 . . 3  |-  F/ y
ph
3 hbeud.1 . . . . 5  |-  ( ph  ->  A. x ph )
43nfi 1392 . . . 4  |-  F/ x ph
5 hbeud.3 . . . 4  |-  ( ph  ->  ( ps  ->  A. x ps ) )
64, 5nfd 1457 . . 3  |-  ( ph  ->  F/ x ps )
72, 6nfeud 1959 . 2  |-  ( ph  ->  F/ x E! y ps )
87nfrd 1454 1  |-  ( ph  ->  ( E! y ps 
->  A. x E! y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1283   E!weu 1943
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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-eu 1946
This theorem is referenced by: (None)
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