Theorem leaddsubi ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		leaddsub	b <= c -> (a + b <= c <-> a <= c - b)
2		letr	b <= a + b -> a + b <= c -> b <= c
3		leaddid2	b <= a + b
4	2, 3	ax_mp	a + b <= c -> b <= c
5	1, 4	syl	a + b <= c -> (a + b <= c <-> a <= c - b)
6		id	a + b <= c -> a + b <= c
7	5, 6	mpbid	a + b <= c -> a <= c - b

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)