Theorem sucsub1 ≪ | index | src | ≫

theorem sucsub1 (a: nat): $ suc a - 1 = a $;

Step	Hyp	Ref	Expression
1		eqtr3	a + 1 - 1 = suc a - 1 -> a + 1 - 1 = a -> suc a - 1 = a
2		subeq1	a + 1 = suc a -> a + 1 - 1 = suc a - 1
3		add12	a + 1 = suc a
4	2, 3	ax_mp	a + 1 - 1 = suc a - 1
5	1, 4	ax_mp	a + 1 - 1 = a -> suc a - 1 = a
6		pncan	a + 1 - 1 = a
7	5, 6	ax_mp	suc a - 1 = 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 (peano2, peano5, addeq, add0, addS)