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Theorem bj-spimt2 31269
Description: A step in the proof of spimt 2063. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-spimt2  |-  ( A. x ( x  =  y  ->  ( ph  ->  ps ) )  -> 
( ( E. x ps  ->  ps )  -> 
( A. x ph  ->  ps ) ) )

Proof of Theorem bj-spimt2
StepHypRef Expression
1 bj-alequex 31268 . . 3  |-  ( A. x ( x  =  y  ->  ( ph  ->  ps ) )  ->  E. x ( ph  ->  ps ) )
2 19.35 1734 . . 3  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
31, 2sylib 199 . 2  |-  ( A. x ( x  =  y  ->  ( ph  ->  ps ) )  -> 
( A. x ph  ->  E. x ps )
)
43imim1d 78 1  |-  ( A. x ( x  =  y  ->  ( ph  ->  ps ) )  -> 
( ( E. x ps  ->  ps )  -> 
( A. x ph  ->  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   E.wex 1657
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  ax-13 2057
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658
This theorem is referenced by:  bj-cbv3ta  31270
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