Theorem eqmaddd ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		eqmtr	mod(n): a + c = b + c -> mod(n): b + c = b + d -> mod(n): a + c = b + d
2		hyp h1	G -> mod(n): a = b
3	2	eqmadd1d	G -> mod(n): a + c = b + c
4		hyp h2	G -> mod(n): c = d
5	4	eqmadd2d	G -> mod(n): b + c = b + d
6	1, 3, 5	sylc	G -> mod(n): a + c = 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 (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)