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Theorem alrimdh 1673
Description: Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 1906 and 19.21h 1908. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Hypotheses
Ref Expression
alrimdh.1  |-  ( ph  ->  A. x ph )
alrimdh.2  |-  ( ps 
->  A. x ps )
alrimdh.3  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
alrimdh  |-  ( ph  ->  ( ps  ->  A. x ch ) )

Proof of Theorem alrimdh
StepHypRef Expression
1 alrimdh.2 . 2  |-  ( ps 
->  A. x ps )
2 alrimdh.1 . . 3  |-  ( ph  ->  A. x ph )
3 alrimdh.3 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
42, 3alimdh 1639 . 2  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
51, 4syl5 32 1  |-  ( ph  ->  ( ps  ->  A. x ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1393
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1619  ax-4 1632
This theorem is referenced by:  alrimdv  1722  ax12indn  2274  gen21nv  33592
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