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Theorem imim1 72
Description: A closed form of syllogism (see syl 17). 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 21 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21imim1d 71 1  |-  ( (
ph  ->  ps )  -> 
( ( ps  ->  ch )  ->  ( ph  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6
This theorem is referenced by:  pm2.83  73  looinv  176  pm3.33  571  tbw-ax1  1460  immo  2159  intss  3781  tb-ax1  23991  3ax5VD  27328  syl5impVD  27329  hbimpgVD  27370  hbalgVD  27371  a9e2ndeqVD  27375  2sb5ndVD  27376
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-mp 10
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