Theorem wl-luk-con4i 34710

Description: Inference rule. Copy of con4i 114 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 34704	. . 3 ⊢ (𝜓 → (¬ 𝜓 → 𝜑))
3	1, 2	wl-luk-imtrid 34708	. 2 ⊢ (𝜓 → (¬ 𝜑 → 𝜑))
4	3	wl-luk-pm2.18d 34709	1 ⊢ (𝜓 → 𝜑)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 34702  ax-luk2 34703  ax-luk3 34704

This theorem is referenced by:  wl-luk-a1i  34712