Theorem wl-luk-ja

Description: Inference joining the antecedents of two premises. Copy of ja with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	wl-luk-ja.1	⊢ ( ¬ 𝜑 → 𝜒 )
	wl-luk-ja.2	⊢ ( 𝜓 → 𝜒 )
Assertion	wl-luk-ja	⊢ ( ( 𝜑 → 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		wl-luk-ja.1	⊢ ( ¬ 𝜑 → 𝜒 )
2		wl-luk-ja.2	⊢ ( 𝜓 → 𝜒 )
3	1	wl-luk-con1i	⊢ ( ¬ 𝜒 → 𝜑 )
4	2	wl-luk-imim2i	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) )
5	3 4	wl-luk-imtrid	⊢ ( ( 𝜑 → 𝜓 ) → ( ¬ 𝜒 → 𝜒 ) )
6	5	wl-luk-pm2.18d	⊢ ( ( 𝜑 → 𝜓 ) → 𝜒 )