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Theorem alimdh 1683
Description: Deduction form of Theorem 19.20 of [Margaris] p. 90, see alim 1677. (Contributed by NM, 4-Jan-2002.)
Hypotheses
Ref Expression
alimdh.1  |-  ( ph  ->  A. x ph )
alimdh.2  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
alimdh  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)

Proof of Theorem alimdh
StepHypRef Expression
1 alimdh.1 . 2  |-  ( ph  ->  A. x ph )
2 alimdh.2 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32al2imi 1681 . 2  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
41, 3syl 17 1  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1663  ax-4 1676
This theorem is referenced by:  alrimdh  1717  alimdv  1757  hbald  1902  alimd  1931  dral1-o  32443  ax12indalem  32485  ax12inda2ALT  32486
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