Theorem mpid

Description: A nested modus ponens deduction. Deduction associated with mpi . (Contributed by NM, 14-Dec-2004)

	Ref	Expression
Hypotheses	mpid.1	$$⊢\phi \to \chi$$
	mpid.2	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
Assertion	mpid	$$⊢\phi \to \left(\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		mpid.1	$$⊢\phi \to \chi$$
2		mpid.2	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
3	1	a1d	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	3 2	mpdd	$$⊢\phi \to \left(\psi \to \theta \right)$$