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Theorem 3ax5 28300
Description: ax-5 1544 for a 3 element left-nested implication. Derived automatically from 3ax5VD 28638. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
3ax5  |-  ( A. x ( ph  ->  ( ps  ->  ch )
)  ->  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) ) )

Proof of Theorem 3ax5
StepHypRef Expression
1 ax-5 1544 . 2  |-  ( A. x ( ph  ->  ( ps  ->  ch )
)  ->  ( A. x ph  ->  A. x
( ps  ->  ch ) ) )
2 ax-5 1544 . 2  |-  ( A. x ( ps  ->  ch )  ->  ( A. x ps  ->  A. x ch ) )
31, 2syl6 29 1  |-  ( A. x ( ph  ->  ( ps  ->  ch )
)  ->  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem is referenced by:  19.41rgVD  28678
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-5 1544
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