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Theorem alimdh 1569
Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (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 1567 . 2  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
41, 3syl 16 1  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1546
This theorem is referenced by:  alrimdh  1594  alimdv  1628  hbald  1747  alimd  1772  dral1  2004  dral1-o  2188  ax11indalem  2231  ax11inda2ALT  2232  hbaldwAUX7  28786  dral1NEW7  28831  sbal1NEW7  28948  ax7w1hAUX7  28978  ax7w2AUX7  28982  ax7w6AUX7  28984  hbaldOLD7  29000
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-gen 1552  ax-5 1563
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