Theorem le02 ≪ | index | src | ≫

theorem le02 (a: nat): $ a <= 0 <-> a = 0 $;

Step	Hyp	Ref	Expression
1		le01	0 <= a
2		leasym	a <= 0 -> 0 <= a -> a = 0
3	1, 2	mpi	a <= 0 -> a = 0
4		eqle	a = 0 -> a <= 0
5	3, 4	ibii	a <= 0 <-> 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)