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Theorem alimd 1746
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 1744 . 2  |-  ( ph  ->  A. x ph )
3 alimd.2 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
42, 3alimdh 1551 1  |-  ( ph  ->  ( A. x 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:  alrimdd  1750  nfimd  1763  spimt  1917  sbied  1982  sb9i  2034  mo  2167  2mo  2223  ralimdaa  2622  axpowndlem3  8217  axext4dist  23559  pm11.71  26996
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
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