Theorem zeqmsub1 ≪ | index | src | ≫

theorem zeqmsub1 (a b c n: nat):
  $ modZ(n): a -Z c = b -Z c <-> modZ(n): a = b $;

Step	Hyp	Ref	Expression
1		zeqmadd1	modZ(n): a +Z -uZ c = b +Z -uZ c <-> modZ(n): a = b
2	1	conv zsub	modZ(n): a -Z c = b -Z c <-> 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)