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Theorem alimdh 1553
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 1551 . 2  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
41, 3syl 15 1  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530
This theorem is referenced by:  alrimdh  1577  alimdv  1611  hbald  1726  alimd  1756  dral1  1918  dral1-o  2106  ax11indalem  2149  ax11inda2ALT  2150  hbaldwAUX7  29425  dral1NEW7  29470  ax7w1hAUX7  29616  ax7w2AUX7  29620  ax7w6AUX7  29622  hbaldOLD7  29638  ax9vax9  29780
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-gen 1536  ax-5 1547
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