Theorem eqzeqm | index | src |

theorem eqzeqm (a b n: nat): $ a = b -> modZ(n): a = b $;
StepHypRefExpression
1 zeqmid
modZ(n): a = a
2 zeqmeq3
a = b -> (modZ(n): a = a <-> modZ(n): a = b)
3 1, 2 mpbii
a = b -> modZ(n): a = b

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)