Theorem wl-luk-imim2i 38105

Description: Inference adding common antecedents in an implication. Copy of imim2i 17 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-luk-imim2i.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
wl-luk-imim2i	⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓))

Proof of Theorem wl-luk-imim2i

Step	Hyp	Ref	Expression
1		wl-luk-imim2i.1	. 2 ⊢ (𝜑 → 𝜓)
2		ax-luk1 38093	. 2 ⊢ ((𝜒 → 𝜑) → ((𝜑 → 𝜓) → (𝜒 → 𝜓)))
3	1, 2	wl-luk-mpi 38104	1 ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-luk1 38093  ax-luk2 38094  ax-luk3 38095

This theorem is used by:  wl-luk-imtrdi  38106  wl-luk-ja  38113  wl-impchain-mp-1  38123  wl-impchain-mp-2  38124