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Theorem alimd 1926
Description: Deduction form of Theorem 19.20 of [Margaris] p. 90, see alim 1679. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
alimd.1  |-  F/ x ph
alimd.2  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
alimd  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)

Proof of Theorem alimd
StepHypRef Expression
1 alimd.1 . . 3  |-  F/ x ph
21nfri 1924 . 2  |-  ( ph  ->  A. x ph )
3 alimd.2 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
42, 3alimdh 1685 1  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   F/wnf 1663
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-12 1904
This theorem depends on definitions:  df-bi 188  df-ex 1660  df-nf 1664
This theorem is referenced by:  alrimdd  1930  mo3  2301  2mo  2345  2moOLD  2346  ralimdaaOLD  2826  axpowndlem3  9013  axext4dist  30275  bj-mo3OLD  31239  pm11.71  36432
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