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Theorem 19.23tOLD 1969
Description: Obsolete proof of 19.23t 1968 as of 13-Aug-2020. (Contributed by NM, 7-Nov-2005.) (Proof shortened by Wolf Lammen, 2-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
19.23tOLD  |-  ( F/ x ps  ->  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) ) )

Proof of Theorem 19.23tOLD
StepHypRef Expression
1 exim 1700 . . 3  |-  ( A. x ( ph  ->  ps )  ->  ( E. x ph  ->  E. x ps ) )
2 19.9t 1946 . . . 4  |-  ( F/ x ps  ->  ( E. x ps  <->  ps )
)
32biimpd 210 . . 3  |-  ( F/ x ps  ->  ( E. x ps  ->  ps ) )
41, 3syl9r 74 . 2  |-  ( F/ x ps  ->  ( A. x ( ph  ->  ps )  ->  ( E. x ph  ->  ps )
) )
5 nfr 1928 . . . 4  |-  ( F/ x ps  ->  ( ps  ->  A. x ps )
)
65imim2d 54 . . 3  |-  ( F/ x ps  ->  (
( E. x ph  ->  ps )  ->  ( E. x ph  ->  A. x ps ) ) )
7 19.38 1706 . . 3  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )
86, 7syl6 34 . 2  |-  ( F/ x ps  ->  (
( E. x ph  ->  ps )  ->  A. x
( ph  ->  ps )
) )
94, 8impbid 193 1  |-  ( F/ x ps  ->  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187   A.wal 1435   E.wex 1657   F/wnf 1661
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909
This theorem depends on definitions:  df-bi 188  df-ex 1658  df-nf 1662
This theorem is referenced by: (None)
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