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Theorem wl-imim2 33697
Description: A closed form of syllogism (see syl 17). Theorem *2.05 of [WhiteheadRussell] p. 100. Copy of imim2 58 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
wl-imim2 ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓)))

Proof of Theorem wl-imim2
StepHypRef Expression
1 ax-luk1 33676 . 2 ((𝜒𝜑) → ((𝜑𝜓) → (𝜒𝜓)))
21wl-com12 33693 1 ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 33676  ax-luk2 33677  ax-luk3 33678
This theorem is referenced by:  wl-ax2  33699
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