Theorem zeqmadd2d ≪ | index | src | ≫

theorem zeqmadd2d (G: wff) (a b c n: nat):
  $ G -> modZ(n): b = c $ >
  $ G -> modZ(n): a +Z b = a +Z c $;

Step	Hyp	Ref	Expression
1		zeqmadd2	modZ(n): a +Z b = a +Z c <-> modZ(n): b = c
2		hyp h	G -> modZ(n): b = c
3	1, 2	sylibr	G -> modZ(n): a +Z b = a +Z c

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)