Theorem wl-luk-mpi 38104

Description: A nested modus ponens inference. Copy of mpi 21 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
wl-luk-mpi	⊢ (𝜑 → 𝜒)

Proof of Theorem wl-luk-mpi

Step	Hyp	Ref	Expression
1		wl-luk-mpi.1	. . . 4 ⊢ 𝜓
2	1	wl-luk-a1i 38103	. . 3 ⊢ (¬ 𝜒 → 𝜓)
3		wl-luk-mpi.2	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
4	2, 3	wl-luk-imtrid 38099	. 2 ⊢ (𝜑 → (¬ 𝜒 → 𝜒))
5	4	wl-luk-pm2.18d 38100	1 ⊢ (𝜑 → 𝜒)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-luk1 38093  ax-luk2 38094  ax-luk3 38095

This theorem is used by:  wl-luk-imim2i  38105