Theorem zadd01 ≪ | index | src | ≫

theorem zadd01 (a: nat): $ 0 +Z a = a $;

Step	Hyp	Ref	Expression
1		eqtr	0 +Z a = a +Z 0 -> a +Z 0 = a -> 0 +Z a = a
2		zaddcom	0 +Z a = a +Z 0
3	1, 2	ax_mp	a +Z 0 = a -> 0 +Z a = a
4		zadd02	a +Z 0 = a
5	3, 4	ax_mp	0 +Z a = 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_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)