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Theorem bj-spst 31294
Description: Closed form of sps 1945. Once in main part, prove sps 1945 and spsd 1947 from it. (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-spst  |-  ( (
ph  ->  ps )  -> 
( A. x ph  ->  ps ) )

Proof of Theorem bj-spst
StepHypRef Expression
1 sp 1939 . 2  |-  ( A. x ph  ->  ph )
21imim1i 60 1  |-  ( (
ph  ->  ps )  -> 
( A. x ph  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1444
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-12 1935
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1666
This theorem is referenced by: (None)
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