Theorem ltpr2tr ≪ | index | src | ≫

theorem ltpr2tr (a b c: nat): $ a < c $ > $ a < b, c $;

Step	Hyp	Ref	Expression
1		ltletr	a < c -> c <= b, c -> a < b, c
2		hyp h	a < c
3	1, 2	ax_mp	c <= b, c -> a < b, c
4		leprid2	c <= b, c
5	3, 4	ax_mp	a < b, 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_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)