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Theorem imim2 54
Description: A closed form of syllogism (see syl 14). Theorem *2.05 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 6-Sep-2012.)
Assertion
Ref Expression
imim2 ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓)))

Proof of Theorem imim2
StepHypRef Expression
1 id 19 . 2 ((𝜑𝜓) → (𝜑𝜓))
21imim2d 53 1 ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  syldd  66  pm3.34  338  spimth  1670  spsbim  1771  elabgft1  11335  bj-rspgt  11343  bj-findis  11531
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