Theorem anmp

Description: Modus ponens for { \/ , -. } axiom systems. (Contributed by Anthony Hart, 12-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	anmp.min	$$⊢\phi$$
	anmp.maj	$$⊢\left(\neg \phi \vee \psi \right)$$
Assertion	anmp	$$⊢\psi$$

Proof

Step	Hyp	Ref	Expression
1		anmp.min	$$⊢\phi$$
2		anmp.maj	$$⊢\left(\neg \phi \vee \psi \right)$$
3	2	imorri	$$⊢\phi \to \psi$$
4	1 3	ax-mp	$$⊢\psi$$