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	⊢ 𝜑
	anmp.maj	⊢ ( ¬ 𝜑 ∨ 𝜓 )
Assertion	anmp	⊢ 𝜓

Proof

Step	Hyp	Ref	Expression
1		anmp.min	⊢ 𝜑
2		anmp.maj	⊢ ( ¬ 𝜑 ∨ 𝜓 )
3	2	imorri	⊢ ( 𝜑 → 𝜓 )
4	1 3	ax-mp	⊢ 𝜓