Theorem wl-luk-imim2 38283

Description: A closed form of syllogism (see syl 18). Theorem *2.05 of [WhiteheadRussell] p. 100. Copy of imim2 59 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
wl-luk-imim2	⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))

Proof of Theorem wl-luk-imim2

Step	Hyp	Ref	Expression
1		ax-luk1 38262	. 2 ⊢ ((𝜒 → 𝜑) → ((𝜑 → 𝜓) → (𝜒 → 𝜓)))
2	1	wl-luk-com12 38279	1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-luk1 38262  ax-luk2 38263  ax-luk3 38264

This theorem is used by:  wl-luk-ax2  38285