Theorem zeqmtrd ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		zeqmtr	modZ(n): a = b -> modZ(n): b = c -> modZ(n): a = c
2		hyp h1	G -> modZ(n): a = b
3		hyp h2	G -> modZ(n): b = c
4	1, 2, 3	sylc	G -> modZ(n): a = 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)