Theorem wl-luk-a1i 38185

Description: Inference rule. Copy of a1i 11 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-luk-a1i.1	⊢ 𝜑

Assertion

Ref	Expression
wl-luk-a1i	⊢ (𝜓 → 𝜑)

Proof of Theorem wl-luk-a1i

Step	Hyp	Ref	Expression
1		wl-luk-a1i.1	. . 3 ⊢ 𝜑
2	1	wl-luk-pm2.24i 38184	. 2 ⊢ (¬ 𝜑 → ¬ 𝜓)
3	2	wl-luk-con4i 38183	1 ⊢ (𝜓 → 𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-luk1 38175  ax-luk2 38176  ax-luk3 38177

This theorem is used by:  wl-luk-mpi  38186  wl-impchain-a1-1  38217