Theorem mpd

Description: A modus ponens deduction. A translation of natural deduction rule -> E ( -> elimination), see natded . Deduction form of ax-mp . Inference associated with a2i . Commuted form of mpcom . (Contributed by NM, 29-Dec-1992)

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

Proof

Step	Hyp	Ref	Expression
1		mpd.1	$$⊢\phi \to \psi$$
2		mpd.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	2	a2i	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)$$
4	1 3	ax-mp	$$⊢\phi \to \chi$$