Theorem wl-imim2 32438

Description: A closed form of syllogism (see syl 17). Theorem *2.05 of [WhiteheadRussell] p. 100. Copy of imim2 56 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

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

Proof of Theorem wl-imim2

Step	Hyp	Ref	Expression
1		ax-luk1 32417	. 2 ⊢ ((𝜒 → 𝜑) → ((𝜑 → 𝜓) → (𝜒 → 𝜓)))
2	1	wl-com12 32434	1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 32417  ax-luk2 32418  ax-luk3 32419

This theorem is referenced by:  wl-ax2  32440