Theorem wl-luk-con1i

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

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

Proof

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