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

Theorem exlimdh 1785
Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 28-Jan-1997.)
Hypotheses
Ref Expression
exlimdh.1  |-  ( ph  ->  A. x ph )
exlimdh.2  |-  ( ch 
->  A. x ch )
exlimdh.3  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
exlimdh  |-  ( ph  ->  ( E. x ps 
->  ch ) )

Proof of Theorem exlimdh
StepHypRef Expression
1 exlimdh.1 . . 3  |-  ( ph  ->  A. x ph )
21nfi 1556 . 2  |-  F/ x ph
3 exlimdh.2 . . 3  |-  ( ch 
->  A. x ch )
43nfi 1556 . 2  |-  F/ x ch
5 exlimdh.3 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
62, 4, 5exlimd 1784 1  |-  ( ph  ->  ( E. x ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   E.wex 1537
This theorem is referenced by:  exlimexi  26980  eexinst01  26982  eexinst11  26983  ax12-2  27792  a12studyALT  27822  a12study3  27824
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
  Copyright terms: Public domain W3C validator