Theorem wl-luk-imim2i 35581

Description: Inference adding common antecedents in an implication. Copy of imim2i 16 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 35569	. 2 ⊢ ((𝜒 → 𝜑) → ((𝜑 → 𝜓) → (𝜒 → 𝜓)))
3	1, 2	wl-luk-mpi 35580	1 ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 35569  ax-luk2 35570  ax-luk3 35571

This theorem is referenced by:  wl-luk-imtrdi  35582  wl-luk-ja  35589  wl-impchain-mp-1  35599  wl-impchain-mp-2  35600