Theorem ltnlt ≪ | index | src | ≫

theorem ltnlt (a b: nat): $ a < b -> ~b < a $;

Step	Hyp	Ref	Expression
1		ltnle	a < b <-> ~b <= a
2		con3	(b < a -> b <= a) -> ~b <= a -> ~b < a
3		ltle	b < a -> b <= a
4	2, 3	ax_mp	~b <= a -> ~b < a
5	1, 4	sylbi	a < b -> ~b < a

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_peano (peano1, peano2, peano5, addeq, add0, addS)