Theorem ins02 ≪ | index | src | ≫

theorem ins02 (a: nat): $ a ; 0 = sn a $;

Step	Hyp	Ref	Expression
1		axext	a ; 0 == sn a -> a ; 0 = sn a
2		eqstr	a ; 0 == sn a u. 0 -> sn a u. 0 == sn a -> a ; 0 == sn a
3		insunsn	a ; 0 == sn a u. 0
4	2, 3	ax_mp	sn a u. 0 == sn a -> a ; 0 == sn a
5		un02	sn a u. 0 == sn a
6	4, 5	ax_mp	a ; 0 == sn a
7	1, 6	ax_mp	a ; 0 = sn 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)