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	$$⊢\neg \phi \to \chi$$
	wl-luk-ja.2	$$⊢\psi \to \chi$$
Assertion	wl-luk-ja	$$⊢\left(\phi \to \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		wl-luk-ja.1	$$⊢\neg \phi \to \chi$$
2		wl-luk-ja.2	$$⊢\psi \to \chi$$
3	1	wl-luk-con1i	$$⊢\neg \chi \to \phi$$
4	2	wl-luk-imim2i	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)$$
5	3 4	wl-luk-imtrid	$$⊢\left(\phi \to \psi \right)\to \left(\neg \chi \to \chi \right)$$
6	5	wl-luk-pm2.18d	$$⊢\left(\phi \to \psi \right)\to \chi$$