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Theorem alrimd 1761
Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (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 10 . 2  |-  ( ph  ->  F/ x ps )
4 alrimd.3 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
51, 3, 4alrimdd 1760 1  |-  ( ph  ->  ( ps  ->  A. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   F/wnf 1534
This theorem is referenced by:  moexex  2225  ralrimd  2644  pssnn  7097  fiint  7149  pm14.24  27735  a12study  29754
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-nf 1535
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