Theorem npcan ≪ | index | src | ≫ 

theorem npcan (a b: nat): $ b <= a -> a - b + b = a $;
StepHypRefExpression
1 addcom 
a - b + b = b + (a - b)
2 pncan3 
b <= a -> b + (a - b) = a
3 1, 2 syl5eq 
b <= a -> a - b + b = a

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, peano5, addeq, add0, addS)