Theorem eqmeq23d ≪ | index | src | ≫

theorem eqmeq23d (G: wff) (a b c d n: nat):
  $ G -> a = b $ >
  $ G -> c = d $ >
  $ G -> (mod(n): a = c <-> mod(n): b = d) $;

Step	Hyp	Ref	Expression
1		eqidd	G -> n = n
2		hyp h1	G -> a = b
3		hyp h2	G -> c = d
4	1, 2, 3	eqmeqd	G -> (mod(n): a = c <-> mod(n): b = d)

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)