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Theorem imim1 70
Description: A closed form of syllogism (see syl 15). Theorem *2.06 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 25-May-2013.)
Assertion
Ref Expression
imim1  |-  ( (
ph  ->  ps )  -> 
( ( ps  ->  ch )  ->  ( ph  ->  ch ) ) )

Proof of Theorem imim1
StepHypRef Expression
1 id 19 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21imim1d 69 1  |-  ( (
ph  ->  ps )  -> 
( ( ps  ->  ch )  ->  ( ph  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  pm2.83  71  looinv  174  pm3.33  568  tbw-ax1  1455  moim  2202  intss  3899  tb-ax1  24889  3ax5VD  28954  syl5impVD  28955  hbimpgVD  28996  hbalgVD  28997  a9e2ndeqVD  29001  2sb5ndVD  29002
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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