Theorem the01 ≪ | index | src | ≫

theorem the01: $ the 0 = 0 $;

Step	Hyp	Ref	Expression
1		absurd	~x e. 0 -> x e. 0 -> x = 0
2		el02	~x e. 0
3	1, 2	ax_mp	x e. 0 -> x = 0
4	3	a1i	T. -> x e. 0 -> x = 0
5	4	eqthe0d	T. -> the 0 = 0
6	5	trud	the 0 = 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_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)