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Theorem imim1 79
Description: A closed form of syllogism (see syl 17). Theorem *2.06 of [WhiteheadRussell] p. 100. Its associated inference is imim1i 60. (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 78 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  80  looinv  186  pm3.33  588  tbw-ax1  1582  moim  2347  intssOLD  4255  mrcmndind  16606  tb-ax1  31032  bj-imim21  31155  al2imVD  37253  syl5impVD  37254  hbimpgVD  37295  hbalgVD  37296  ax6e2ndeqVD  37300  2sb5ndVD  37301
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