Theorem muldiv1 | index | src |

theorem muldiv1 (a b: nat): $ b != 0 -> a * b // b = a $;
StepHypRefExpression
1 mulcom
a * b = b * a
2 1 a1i
b != 0 -> a * b = b * a
3 eqidd
b != 0 -> b = b
4 2, 3 diveqd
b != 0 -> a * b // b = b * a // b
5 muldiv2
b != 0 -> b * a // b = a
6 4, 5 eqtrd
b != 0 -> a * b // b = a

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)