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

Theorem alrimdd 1749
Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
alrimdd.1  |-  F/ x ph
alrimdd.2  |-  ( ph  ->  F/ x ps )
alrimdd.3  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
alrimdd  |-  ( ph  ->  ( ps  ->  A. x ch ) )

Proof of Theorem alrimdd
StepHypRef Expression
1 alrimdd.2 . . 3  |-  ( ph  ->  F/ x ps )
21nfrd 1744 . 2  |-  ( ph  ->  ( ps  ->  A. x ps ) )
3 alrimdd.1 . . 3  |-  F/ x ph
4 alrimdd.3 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
53, 4alimd 1745 . 2  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
62, 5syld 42 1  |-  ( ph  ->  ( ps  ->  A. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1528   F/wnf 1532
This theorem is referenced by:  alrimd  1750  19.23t  1797
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-11 1716
This theorem depends on definitions:  df-bi 179  df-nf 1533
  Copyright terms: Public domain W3C validator