Theorem zmul12 | index | src |

theorem zmul12 (a: nat): $ a *Z b0 1 = a $;
StepHypRefExpression
1 eqtr
a *Z b0 1 = b0 1 *Z a -> b0 1 *Z a = a -> a *Z b0 1 = a
2 zmulcom
a *Z b0 1 = b0 1 *Z a
3 1, 2 ax_mp
b0 1 *Z a = a -> a *Z b0 1 = a
4 zmul11
b0 1 *Z a = a
5 3, 4 ax_mp
a *Z b0 1 = 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)