Theorem ltaddsub2 ≪ | index | src | ≫

theorem ltaddsub2 (a b c: nat): $ a + b < c <-> b < c - a $;

Step	Hyp	Ref	Expression
1		bitr	(a + b < c <-> b + a < c) -> (b + a < c <-> b < c - a) -> (a + b < c <-> b < c - a)
2		lteq1	a + b = b + a -> (a + b < c <-> b + a < c)
3		addcom	a + b = b + a
4	2, 3	ax_mp	a + b < c <-> b + a < c
5	1, 4	ax_mp	(b + a < c <-> b < c - a) -> (a + b < c <-> b < c - a)
6		ltaddsub	b + a < c <-> b < c - a
7	5, 6	ax_mp	a + b < c <-> b < c - 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, add0, addS)