Theorem wl-luk-con4i 38101

Description: Inference rule. Copy of con4i 115 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-luk-con4i.1	⊢ (¬ 𝜑 → ¬ 𝜓)

Assertion

Ref	Expression
wl-luk-con4i	⊢ (𝜓 → 𝜑)

Proof of Theorem wl-luk-con4i

Step	Hyp	Ref	Expression
1		wl-luk-con4i.1	. . 3 ⊢ (¬ 𝜑 → ¬ 𝜓)
2		ax-luk3 38095	. . 3 ⊢ (𝜓 → (¬ 𝜓 → 𝜑))
3	1, 2	wl-luk-imtrid 38099	. 2 ⊢ (𝜓 → (¬ 𝜑 → 𝜑))
4	3	wl-luk-pm2.18d 38100	1 ⊢ (𝜓 → 𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → 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-a1i  38103