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Theorem alsi1d 10950
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 10947 . . 3  |-  ( A.! x ( ps  ->  ch )  <->  ( A. x
( ps  ->  ch )  /\  E. x ps ) )
31, 2sylib 120 . 2  |-  ( ph  ->  ( A. x ( ps  ->  ch )  /\  E. x ps )
)
43simpld 110 1  |-  ( ph  ->  A. x ( ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   A.wal 1283   E.wex 1422   A.!walsi 10945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115  df-alsi 10947
This theorem is referenced by: (None)
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