Theorem and_to_or ≪ | index | src | ≫

\and蕴涵\or

theorem and_to_or (A B: wff): $ A \and B \imp A \or B $;

Step	Hyp	Ref	Expression
1		imp_tran	(A \and B \imp A) \imp (A \imp A \or B) \imp A \and B \imp A \or B
2		and_splitl	A \and B \imp A
3	1, 2	ax_mp	(A \imp A \or B) \imp A \and B \imp A \or B
4		intror_or	A \imp A \or B
5	3, 4	ax_mp	A \and B \imp A \or B

Axiom use

Logic (ax_mp, ax_1, ax_2, ax_3)