Theorem wl-mpi 32428

Description: A nested modus ponens inference. Copy of mpi 20 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
wl-mpi	⊢ (𝜑 → 𝜒)

Proof of Theorem wl-mpi

Step	Hyp	Ref	Expression
1		wl-mpi.1	. . . 4 ⊢ 𝜓
2	1	wl-a1i 32427	. . 3 ⊢ (¬ 𝜒 → 𝜓)
3		wl-mpi.2	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
4	2, 3	wl-syl5 32423	. 2 ⊢ (𝜑 → (¬ 𝜒 → 𝜒))
5	4	wl-pm2.18d 32424	1 ⊢ (𝜑 → 𝜒)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 32417  ax-luk2 32418  ax-luk3 32419

This theorem is referenced by:  wl-imim2i  32429