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Theorem alrimdd 1748
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 1743 . 2  |-  ( ph  ->  ( ps  ->  A. x ps ) )
3 alrimdd.1 . . 3  |-  F/ x ph
4 alrimdd.3 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
53, 4alimd 1744 . 2  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
62, 5syld 40 1  |-  ( ph  ->  ( ps  ->  A. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   F/wnf 1531
This theorem is referenced by:  alrimd  1749  19.23t  1796
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-11 1715
This theorem depends on definitions:  df-bi 177  df-nf 1532
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