Theorem zdvdmul2 ≪ | index | src | ≫

theorem zdvdmul2 (a b: nat): $ a |Z a *Z b $;

Step	Hyp	Ref	Expression
1		zdvdeq2	b Z a = a Z b -> (a \|Z b Z a <-> a \|Z a Z b)
2		zmulcom	b Z a = a Z b
3	1, 2	ax_mp	a \|Z b Z a <-> a \|Z a Z b
4		zdvdmul1	a \|Z b *Z a
5	3, 4	mpbi	a \|Z a *Z b

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)