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Theorem imim1 70
Description: A closed form of syllogism (see syl 14). 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 ((φψ) → ((ψχ) → (φχ)))

Proof of Theorem imim1
StepHypRef Expression
1 id 19 . 2 ((φψ) → (φψ))
21imim1d 69 1 ((φψ) → ((ψχ) → (φχ)))
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:  pm2.83  71  pm3.33  327  looinvdc  820  intss  3627
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