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Theorem al2im 1656
Description: Closed form of al2imi 1657. Version of ax-4 1652 for a nested implication. (Contributed by Alan Sare, 31-Dec-2011.)
Assertion
Ref Expression
al2im  |-  ( A. x ( ph  ->  ( ps  ->  ch )
)  ->  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) ) )

Proof of Theorem al2im
StepHypRef Expression
1 alim 1653 . 2  |-  ( A. x ( ph  ->  ( ps  ->  ch )
)  ->  ( A. x ph  ->  A. x
( ps  ->  ch ) ) )
2 alim 1653 . 2  |-  ( A. x ( ps  ->  ch )  ->  ( A. x ps  ->  A. x ch ) )
31, 2syl6 31 1  |-  ( A. x ( ph  ->  ( ps  ->  ch )
)  ->  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1403
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1652
This theorem is referenced by:  al2imi  1657  bj-alanim  30768  al3im  35625  19.41rgVD  36733
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