Theorem zdvdeq1d ≪ | index | src | ≫

theorem zdvdeq1d (_G: wff) (_m1 _m2 n: nat):
  $ _G -> _m1 = _m2 $ >
  $ _G -> (_m1 |Z n <-> _m2 |Z n) $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> _m1 = _m2
2		eqidd	_G -> n = n
3	1, 2	zdvdeqd	_G -> (_m1 \|Z n <-> _m2 \|Z n)

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 (peano2, addeq, muleq)