Theorem wl-luk-ja 37440

Description: Inference joining the antecedents of two premises. Copy of ja 186 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
wl-luk-ja	⊢ ((𝜑 → 𝜓) → 𝜒)

Proof of Theorem wl-luk-ja

Step	Hyp	Ref	Expression
1		wl-luk-ja.1	. . . 4 ⊢ (¬ 𝜑 → 𝜒)
2	1	wl-luk-con1i 37439	. . 3 ⊢ (¬ 𝜒 → 𝜑)
3		wl-luk-ja.2	. . . 4 ⊢ (𝜓 → 𝜒)
4	3	wl-luk-imim2i 37432	. . 3 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒))
5	2, 4	wl-luk-imtrid 37426	. 2 ⊢ ((𝜑 → 𝜓) → (¬ 𝜒 → 𝜒))
6	5	wl-luk-pm2.18d 37427	1 ⊢ ((𝜑 → 𝜓) → 𝜒)

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-ax2  37443