Theorem lt02 ≪ | index | src | ≫

theorem lt02 (a: nat): $ ~a < 0 $;

Step	Hyp	Ref	Expression
1		con3	(a < 0 -> suc a = 0) -> ~suc a = 0 -> ~a < 0
2		bi1	(a < 0 <-> suc a = 0) -> a < 0 -> suc a = 0
3		le02	suc a <= 0 <-> suc a = 0
4	3	conv lt	a < 0 <-> suc a = 0
5	2, 4	ax_mp	a < 0 -> suc a = 0
6	1, 5	ax_mp	~suc a = 0 -> ~a < 0
7		peano1	suc a != 0
8	7	conv ne	~suc a = 0
9	6, 8	ax_mp	~a < 0

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)