Theorem idvd | index | src |

theorem idvd (a b c: nat): $ c * a = b -> a || b $;
StepHypRefExpression
1 muleq1
x = c -> x * a = c * a
2 1 eqeq1d
x = c -> (x * a = b <-> c * a = b)
3 2 iexe
c * a = b -> E. x x * a = b
4 3 conv dvd
c * a = b -> a || b

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_12), axs_peano (muleq)