Theorem zdvdmul11 ≪ | index | src | ≫

theorem zdvdmul11 (a b c: nat): $ a |Z b -> a |Z b *Z c $;

Step	Hyp	Ref	Expression
1		zdvdmul2	b \|Z b *Z c
2		zdvdtr	a \|Z b -> b \|Z b Z c -> a \|Z b Z c
3	1, 2	mpi	a \|Z b -> a \|Z b *Z c

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)