Theorem lt12 ≪ | index | src | ≫

theorem lt12 (a: nat): $ a < 1 <-> a = 0 $;

Step	Hyp	Ref	Expression
1		bitr3	(a <= 0 <-> a < 1) -> (a <= 0 <-> a = 0) -> (a < 1 <-> a = 0)
2		leltsuc	a <= 0 <-> a < suc 0
3	2	conv d1	a <= 0 <-> a < 1
4	1, 3	ax_mp	(a <= 0 <-> a = 0) -> (a < 1 <-> a = 0)
5		le02	a <= 0 <-> a = 0
6	4, 5	ax_mp	a < 1 <-> 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)