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Theorem hbeud 2019
Description: Deduction version of hbeu 2018. (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 1438 . . 3  |-  F/ y
ph
3 hbeud.1 . . . . 5  |-  ( ph  ->  A. x ph )
43nfi 1438 . . . 4  |-  F/ x ph
5 hbeud.3 . . . 4  |-  ( ph  ->  ( ps  ->  A. x ps ) )
64, 5nfd 1503 . . 3  |-  ( ph  ->  F/ x ps )
72, 6nfeud 2013 . 2  |-  ( ph  ->  F/ x E! y ps )
87nfrd 1500 1  |-  ( ph  ->  ( E! y ps 
->  A. x E! y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1329   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: (None)
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