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Theorem imim1 76
Description: A closed form of syllogism (see syl 16). Theorem *2.06 of [WhiteheadRussell] p. 100. (Contributed by NM, 29-Dec-1992.) (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 22 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21imim1d 75 1  |-  ( (
ph  ->  ps )  -> 
( ( ps  ->  ch )  ->  ( ph  ->  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:  pm2.83  77  looinv  182  pm3.33  585  tbw-ax1  1507  moim  2319  intss  4154  mrcmndind  15499  isucn2  19859  tb-ax1  28230  3ax4VD  31603  syl5impVD  31604  hbimpgVD  31645  hbalgVD  31646  ax6e2ndeqVD  31650  2sb5ndVD  31651
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