Theorem add12 ≪ | index | src | ≫

theorem add12 (a: nat): $ a + 1 = suc a $;

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

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7), axs_peano (peano2, add0, addS)