Theorem zmul02 ≪ | index | src | ≫

theorem zmul02 (a: nat): $ a *Z 0 = 0 $;

Step	Hyp	Ref	Expression
1		eqtr	a Z 0 = 0 Z a -> 0 Z a = 0 -> a Z 0 = 0
2		zmulcom	a Z 0 = 0 Z a
3	1, 2	ax_mp	0 Z a = 0 -> a Z 0 = 0
4		zmul01	0 *Z a = 0
5	3, 4	ax_mp	a *Z 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)