Theorem lttr ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		lelttr	a <= b -> b < c -> a < c
2		ltle	a < b -> a <= b
3	1, 2	syl	a < b -> b < c -> a < c

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)