Theorem eqmeq1d ≪ | index | src | ≫

theorem eqmeq1d (_G: wff) (_n1 _n2 a b: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> (mod(_n1): a = b <-> mod(_n2): a = b) $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> _n1 = _n2
2		eqidd	_G -> a = a
3		eqidd	_G -> b = b
4	1, 2, 3	eqmeqd	_G -> (mod(_n1): a = b <-> mod(_n2): 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 (peano2, addeq, muleq)