Theorem imp_refl ≪ | index | src | ≫

同一律

theorem imp_refl (A: wff): $ A \imp A $;


(A \imp (A \imp A) \imp A) \imp (A \imp A \imp A) \imp A \imp A
A \imp (A \imp A) \imp A
(A \imp A \imp A) \imp A \imp A
A \imp A \imp A
A \imp A

Step	Hyp	Ref	Expression
1		imp_imp_insl	(A \imp (A \imp A) \imp A) \imp (A \imp A \imp A) \imp A \imp A
2		introl_imp	A \imp (A \imp A) \imp A
3	1, 2	ax_mp	(A \imp A \imp A) \imp A \imp A
4		introl_imp	A \imp A \imp A
5	3, 4	ax_mp	A \imp A

Axiom use

Logic (ax_mp, ax_1, ax_2)