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Theorem pm2.86 103
Description: Converse of axiom ax-2 7. Theorem *2.86 of [WhiteheadRussell] p. 108. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)
Assertion
Ref Expression
pm2.86  |-  ( ( ( ph  ->  ps )  ->  ( ph  ->  ch ) )  ->  ( ph  ->  ( ps  ->  ch ) ) )

Proof of Theorem pm2.86
StepHypRef Expression
1 id 22 . 2  |-  ( ( ( ph  ->  ps )  ->  ( ph  ->  ch ) )  ->  (
( ph  ->  ps )  ->  ( ph  ->  ch ) ) )
21pm2.86d 102 1  |-  ( ( ( ph  ->  ps )  ->  ( ph  ->  ch ) )  ->  ( ph  ->  ( ps  ->  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  pm2.86iALT  105  imdi  364
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