Theorem thesn ≪ | index | src | ≫

theorem thesn (a: nat): $ the (sn a) = a $;

Step	Hyp	Ref	Expression
1		elsn	a1 e. sn a <-> a1 = a
2	1	a1i	T. -> (a1 e. sn a <-> a1 = a)
3	2	eqthed	T. -> the (sn a) = a
4	3	trud	the (sn a) = 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 (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)