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

Theorem eximdh 1580
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 20-May-1996.)
Hypotheses
Ref Expression
eximdh.1  |-  ( ph  ->  A. x ph )
eximdh.2  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
eximdh  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)

Proof of Theorem eximdh
StepHypRef Expression
1 eximdh.1 . . 3  |-  ( ph  ->  A. x ph )
2 eximdh.2 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2alrimih 1557 . 2  |-  ( ph  ->  A. x ( ps 
->  ch ) )
4 exim 1567 . 2  |-  ( A. x ( ps  ->  ch )  ->  ( E. x ps  ->  E. x ch ) )
53, 4syl 17 1  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   E.wex 1533
This theorem is referenced by:  eximdv  1613  eximd  1754  a9e2eq  27594
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549
This theorem depends on definitions:  df-bi 179  df-ex 1534
  Copyright terms: Public domain W3C validator