Theorem and_splitl ≪ | index | src | ≫

\and左拆分

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

Step	Hyp	Ref	Expression
1		neg_imp_swap	(\neg A \imp A \imp \neg B) \imp \neg (A \imp \neg B) \imp A
2		neg_elimintror_imp	\neg A \imp A \imp \neg B
3	1, 2	ax_mp	\neg (A \imp \neg B) \imp A
4	3	conv and	A \and B \imp A

Axiom use

Logic (ax_mp, ax_1, ax_2, ax_3)