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Theorem bj-nfext 34686
Description: Closed form of nfex 1953. (Contributed by BJ, 10-Oct-2019.)
Assertion
Ref Expression
bj-nfext  |-  ( A. x F/ y ph  ->  F/ y E. x ph )

Proof of Theorem bj-nfext
StepHypRef Expression
1 df-nf 1622 . . . . 5  |-  ( F/ y ph  <->  A. y
( ph  ->  A. y ph ) )
21biimpi 194 . . . 4  |-  ( F/ y ph  ->  A. y
( ph  ->  A. y ph ) )
32alimi 1638 . . 3  |-  ( A. x F/ y ph  ->  A. x A. y (
ph  ->  A. y ph )
)
4 nfa2 1958 . . . 4  |-  F/ y A. x A. y
( ph  ->  A. y ph )
5 bj-hbext 34684 . . . 4  |-  ( A. x A. y ( ph  ->  A. y ph )  ->  ( E. x ph  ->  A. y E. x ph ) )
64, 5alrimi 1882 . . 3  |-  ( A. x A. y ( ph  ->  A. y ph )  ->  A. y ( E. x ph  ->  A. y E. x ph ) )
73, 6syl 16 . 2  |-  ( A. x F/ y ph  ->  A. y ( E. x ph  ->  A. y E. x ph ) )
8 df-nf 1622 . 2  |-  ( F/ y E. x ph  <->  A. y ( E. x ph  ->  A. y E. x ph ) )
97, 8sylibr 212 1  |-  ( A. x F/ y ph  ->  F/ y E. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1396   E.wex 1617   F/wnf 1621
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859
This theorem depends on definitions:  df-bi 185  df-ex 1618  df-nf 1622
This theorem is referenced by: (None)
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