Theorem sbnid ≪ | index | src | ≫

theorem sbnid {x: nat} (a: nat x): $ N[x / x] a = a $;

Step	Hyp	Ref	Expression
1		sbid	[x / x] y = a <-> y = a
2	1	a1i	T. -> ([x / x] y = a <-> y = a)
3	2	eqtheabd	T. -> the {y \| [x / x] y = a} = a
4	3	conv sbn	T. -> N[x / x] a = a
5	4	trud	N[x / x] 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)