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Theorem imim2 58
 Description: A closed form of syllogism (see syl 17). Theorem *2.05 of [WhiteheadRussell] p. 100. Its associated inference is imim2i 16. Its associated deduction is imim2d 57. An alternate proof from more basic results is given by ax-1 6 followed by a2d 29. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 6-Sep-2012.)
Assertion
Ref Expression
imim2 ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓)))

Proof of Theorem imim2
StepHypRef Expression
1 id 22 . 2 ((𝜑𝜓) → (𝜑𝜓))
21imim2d 57 1 ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓)))
 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:  syldd  72  imim12  105  pm3.34  765  axprlem2  5297  jath  33202  bj-peircestab  34316  bj-cbvalimt  34400  bj-cbveximt  34401  19.41rgVD  42016  adh-minim  43995  adh-minimp  44007
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