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Theorem alrimd 1867
Description: Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 1891. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
alrimd.1  |-  F/ x ph
alrimd.2  |-  F/ x ps
alrimd.3  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
alrimd  |-  ( ph  ->  ( ps  ->  A. x ch ) )

Proof of Theorem alrimd
StepHypRef Expression
1 alrimd.1 . 2  |-  F/ x ph
2 alrimd.2 . . 3  |-  F/ x ps
32a1i 11 . 2  |-  ( ph  ->  F/ x ps )
4 alrimd.3 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
51, 3, 4alrimdd 1866 1  |-  ( ph  ->  ( ps  ->  A. x ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1381   F/wnf 1603
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-12 1840
This theorem depends on definitions:  df-bi 185  df-ex 1600  df-nf 1604
This theorem is referenced by:  nfimd  1903  moexex  2349  ralrimd  2847  pssnn  7740  fiint  7799  wl-mo3t  29997  pm14.24  31293
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