Theorem zaddeq2d ≪ | index | src | ≫

theorem zaddeq2d (_G: wff) (m _n1 _n2: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> m +Z _n1 = m +Z _n2 $;

Step	Hyp	Ref	Expression
1		eqidd	_G -> m = m
2		hyp _h	_G -> _n1 = _n2
3	1, 2	zaddeqd	_G -> m +Z _n1 = m +Z _n2

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)