Theorem wl-luk-mpi

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

	Ref	Expression
Hypotheses	wl-luk-mpi.1	$$⊢\psi$$
	wl-luk-mpi.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	wl-luk-mpi	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		wl-luk-mpi.1	$$⊢\psi$$
2		wl-luk-mpi.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	1	wl-luk-a1i	$$⊢\neg \chi \to \psi$$
4	3 2	wl-luk-imtrid	$$⊢\phi \to \left(\neg \chi \to \chi \right)$$
5	4	wl-luk-pm2.18d	$$⊢\phi \to \chi$$