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

Theorem exlimdh 1804
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 1538 . 2  |-  F/ x ph
3 exlimdh.2 . . 3  |-  ( ch 
->  A. x ch )
43nfi 1538 . 2  |-  F/ x ch
5 exlimdh.3 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
62, 4, 5exlimd 1803 1  |-  ( ph  ->  ( E. x ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   E.wex 1528
This theorem is referenced by:  exlimexi  28287  eexinst01  28289  eexinst11  28290  ax12-2  29103  a12studyALT  29133  a12study3  29135
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532
  Copyright terms: Public domain W3C validator