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Theorem imim1 72
Description: A closed form of syllogism (see syl 16). 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 20 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21imim1d 71 1  |-  ( (
ph  ->  ps )  -> 
( ( ps  ->  ch )  ->  ( ph  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  pm2.83  73  looinv  175  pm3.33  569  tbw-ax1  1474  moim  2326  intss  4063  isucn2  18301  tb-ax1  26120  3ax5VD  28901  syl5impVD  28902  hbimpgVD  28943  hbalgVD  28944  a9e2ndeqVD  28948  2sb5ndVD  28949
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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