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Theorem wl-imim2 32234
Description: A closed form of syllogism (see syl 17). Theorem *2.05 of [WhiteheadRussell] p. 100. Copy of imim2 55 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 32213 . 2 ((𝜒𝜑) → ((𝜑𝜓) → (𝜒𝜓)))
21wl-com12 32230 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 32213  ax-luk2 32214  ax-luk3 32215
This theorem is referenced by:  wl-ax2  32236
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