Theorem mp2d

Description: A double modus ponens deduction. Deduction associated with mp2 . (Contributed by NM, 23-May-2013) (Proof shortened by Wolf Lammen, 23-Jul-2013)

	Ref	Expression
Hypotheses	mp2d.1	$$⊢\phi \to \psi$$
	mp2d.2	$$⊢\phi \to \chi$$
	mp2d.3	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
Assertion	mp2d	$$⊢\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mp2d.1	$$⊢\phi \to \psi$$
2		mp2d.2	$$⊢\phi \to \chi$$
3		mp2d.3	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
4	2 3	mpid	$$⊢\phi \to \left(\psi \to \theta \right)$$
5	1 4	mpd	$$⊢\phi \to \theta$$