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

Theorem alimd 1824
Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
alimd.1  |-  F/ x ph
alimd.2  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
alimd  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)

Proof of Theorem alimd
StepHypRef Expression
1 alimd.1 . . 3  |-  F/ x ph
21nfri 1822 . 2  |-  ( ph  ->  A. x ph )
3 alimd.2 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
42, 3alimdh 1618 1  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1377   F/wnf 1599
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-12 1803
This theorem depends on definitions:  df-bi 185  df-ex 1597  df-nf 1600
This theorem is referenced by:  alrimdd  1828  sbiedOLD  2126  sb9iOLD  2151  mo3  2320  mo3OLD  2321  moOLD  2327  2mo  2382  2moOLD  2383  2moOLDOLD  2384  ralimdaaOLD  2867  axpowndlem3  8976  axpowndlem3OLD  8977  ssrelf  27236  axext4dist  29086  pm11.71  31108
  Copyright terms: Public domain W3C validator