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Theorem alsi1d 13236
Description: Deduction rule: Given "all some" applied to a top-level inference, you can extract the "for all" part. (Contributed by David A. Wheeler, 20-Oct-2018.)
Hypothesis
Ref Expression
alsi1d.1  |-  ( ph  ->  A.! x ( ps 
->  ch ) )
Assertion
Ref Expression
alsi1d  |-  ( ph  ->  A. x ( ps 
->  ch ) )

Proof of Theorem alsi1d
StepHypRef Expression
1 alsi1d.1 . . 3  |-  ( ph  ->  A.! x ( ps 
->  ch ) )
2 df-alsi 13233 . . 3  |-  ( A.! x ( ps  ->  ch )  <->  ( A. x
( ps  ->  ch )  /\  E. x ps ) )
31, 2sylib 121 . 2  |-  ( ph  ->  ( A. x ( ps  ->  ch )  /\  E. x ps )
)
43simpld 111 1  |-  ( ph  ->  A. x ( ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103   A.wal 1329   E.wex 1468   A.!walsi 13231
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116  df-alsi 13233
This theorem is referenced by: (None)
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