Theorem zeqmid0 | index | src |

theorem zeqmid0 (n: nat): $ modZ(n): b0 n = 0 $;
StepHypRefExpression
1 zeqm03
modZ(n): b0 n = 0 <-> b0 n |Z b0 n
2 zdvdid
b0 n |Z b0 n
3 1, 2 mpbir
modZ(n): b0 n = 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)