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Theorem alimd 1744
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 1742 . 2  |-  ( ph  ->  A. x ph )
3 alimd.2 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
42, 3alimdh 1550 1  |-  ( ph  ->  ( A. x 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:  alrimdd  1748  nfimd  1761  spimt  1914  sbied  1976  sb9i  2034  mo  2165  2mo  2221  ralimdaa  2620  axpowndlem3  8221  sigaclfu2  23482  axext4dist  24157  pm11.71  27596
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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