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Theorem bj-nexdt 31250
Description: Closed form of nexd 1938. (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-nexdt  |-  ( F/ x ph  ->  ( A. x ( ph  ->  -. 
ps )  ->  ( ph  ->  -.  E. x ps ) ) )

Proof of Theorem bj-nexdt
StepHypRef Expression
1 nfr 1928 . 2  |-  ( F/ x ph  ->  ( ph  ->  A. x ph )
)
2 bj-nexdh 31213 . 2  |-  ( A. x ( ph  ->  -. 
ps )  ->  (
( ph  ->  A. x ph )  ->  ( ph  ->  -.  E. x ps ) ) )
31, 2syl5com 31 1  |-  ( F/ x ph  ->  ( A. x ( ph  ->  -. 
ps )  ->  ( ph  ->  -.  E. x ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   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-12 1909
This theorem depends on definitions:  df-bi 188  df-ex 1658  df-nf 1662
This theorem is referenced by:  bj-nexdvt  31251
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