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Theorem al3im 36208
Description: Version of ax-4 1676 for a nested implication. (Contributed by RP, 13-Apr-2020.)
Assertion
Ref Expression
al3im  |-  ( A. x ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )  ->  ( A. x ph  ->  ( A. x ps  ->  ( A. x ch  ->  A. x th )
) ) )

Proof of Theorem al3im
StepHypRef Expression
1 alim 1677 . 2  |-  ( A. x ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )  ->  ( A. x ph  ->  A. x ( ps 
->  ( ch  ->  th )
) ) )
2 al2im 1680 . 2  |-  ( A. x ( ps  ->  ( ch  ->  th )
)  ->  ( A. x ps  ->  ( A. x ch  ->  A. x th ) ) )
31, 2syl6 34 1  |-  ( A. x ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )  ->  ( A. x ph  ->  ( A. x ps  ->  ( A. x ch  ->  A. x th )
) ) )
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-4 1676
This theorem is referenced by: (None)
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