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Theorem imim1 83
Description: A closed form of syllogism (see syl 17). Theorem *2.06 of [WhiteheadRussell] p. 100. Its associated inference is imim1i 63. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 25-May-2013.)
Assertion
Ref Expression
imim1 ((𝜑𝜓) → ((𝜓𝜒) → (𝜑𝜒)))

Proof of Theorem imim1
StepHypRef Expression
1 id 22 . 2 ((𝜑𝜓) → (𝜑𝜓))
21imim1d 82 1 ((𝜑𝜓) → ((𝜓𝜒) → (𝜑𝜒)))
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  84  peirceroll  85  imim12  105  looinv  204  pm3.33  761  a2and  839  impsingle  1619  tarski-bernays-ax2  1632  tbw-ax1  1692  moim  2619  mndind  17980  tb-ax1  33628  bj-imim21  33783  bj-cbvalimt  33869  bj-cbveximt  33870  al2imVD  41073  syl5impVD  41074  hbimpgVD  41115  hbalgVD  41116  ax6e2ndeqVD  41120  2sb5ndVD  41121
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