Theorem wl-luk-con1i 37439

Description: A contraposition inference. Copy of con1i 147 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-luk-con1i.1	⊢ (¬ 𝜑 → 𝜓)

Assertion

Ref	Expression
wl-luk-con1i	⊢ (¬ 𝜓 → 𝜑)

Proof of Theorem wl-luk-con1i

Step	Hyp	Ref	Expression
1		wl-luk-con1i.1	. . 3 ⊢ (¬ 𝜑 → 𝜓)
2		wl-luk-pm2.21 37438	. . 3 ⊢ (¬ 𝜓 → (𝜓 → 𝜑))
3	1, 2	wl-luk-imtrid 37426	. 2 ⊢ (¬ 𝜓 → (¬ 𝜑 → 𝜑))
4	3	wl-luk-pm2.18d 37427	1 ⊢ (¬ 𝜓 → 𝜑)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 37420  ax-luk2 37421  ax-luk3 37422

This theorem is referenced by:  wl-luk-ja  37440  wl-luk-notnotr  37445