Theorem znegid1 | index | src |

theorem znegid1 (a: nat): $ -uZ a +Z a = 0 $;
StepHypRefExpression
1 eqtr
-uZ a +Z a = a +Z -uZ a -> a +Z -uZ a = 0 -> -uZ a +Z a = 0
2 zaddcom
-uZ a +Z a = a +Z -uZ a
3 1, 2 ax_mp
a +Z -uZ a = 0 -> -uZ a +Z a = 0
4 znegid
a +Z -uZ a = 0
5 3, 4 ax_mp
-uZ a +Z a = 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)