Theorem add11 ≪ | index | src | ≫

theorem add11 (a: nat): $ 1 + a = suc a $;

Step	Hyp	Ref	Expression
1		eqtr	1 + a = suc (0 + a) -> suc (0 + a) = suc a -> 1 + a = suc a
2		addS1	suc 0 + a = suc (0 + a)
3	2	conv d1	1 + a = suc (0 + a)
4	1, 3	ax_mp	suc (0 + a) = suc a -> 1 + a = suc a
5		suceq	0 + a = a -> suc (0 + a) = suc a
6		add01	0 + a = a
7	5, 6	ax_mp	suc (0 + a) = suc a
8	4, 7	ax_mp	1 + a = suc 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_peano (peano2, peano5, addeq, add0, addS)