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Theorem bj-alrimih 31029
Description: The general theorem that alrimih 1689 proves. (Contributed by BJ, 4-Oct-2019.)
Hypotheses
Ref Expression
bj-alrimih.1  |-  ( ph  ->  A. x ps )
bj-alrimih.2  |-  ( ps 
->  ch )
Assertion
Ref Expression
bj-alrimih  |-  ( ph  ->  A. x ch )

Proof of Theorem bj-alrimih
StepHypRef Expression
1 bj-alrimih.2 . . 3  |-  ( ps 
->  ch )
21ax-gen 1665 . 2  |-  A. x
( ps  ->  ch )
3 bj-alrimih.1 . 2  |-  ( ph  ->  A. x ps )
4 bj-alrimh 31028 . 2  |-  ( A. x ( ps  ->  ch )  ->  ( ( ph  ->  A. x ps )  ->  ( ph  ->  A. x ch ) ) )
52, 3, 4mp2 9 1  |-  ( ph  ->  A. x ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1665  ax-4 1678
This theorem is referenced by:  bj-modalbe  31062
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