MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  alimdh Structured version   Unicode version

Theorem alimdh 1572
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 1570 . 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 1549
This theorem is referenced by:  alrimdh  1597  alimdv  1631  hbald  1755  alimd  1780  dral1OLD  2054  dral1-o  2231  ax11indalem  2274  ax11inda2ALT  2275  hbaldwAUX7  29386  dral1NEW7  29431  sbal1NEW7  29553  ax7w1hAUX7  29584  ax7w2AUX7  29588  ax7w6AUX7  29590  hbaldOLD7  29622
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-gen 1555  ax-5 1566
  Copyright terms: Public domain W3C validator