Theorem and_left_split ≪ | index | src | ≫

∧左拆分

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

Step	Hyp	Ref	Expression
1		imp_left_neg_permute	(\neg A \imp A \imp \neg B) \imp \neg (A \imp \neg B) \imp A
2		neg_elim_with_imp	\neg A \imp A \imp \neg B
3	1, 2	mp	\neg (A \imp \neg B) \imp A
4	3	conv and	A \and B \imp A

Axiom use

ZFC (ax_mp, ax_p1, ax_p2, ax_p3)