Theorem ltletrd ≪ | index | src | ≫

theorem ltletrd (G: wff) (a b c: nat):
  $ G -> a < b $ >
  $ G -> b <= c $ >
  $ G -> a < c $;

Step	Hyp	Ref	Expression
1		hyp h1	G -> a < b
2	1	conv lt	G -> suc a <= b
3		hyp h2	G -> b <= c
4	2, 3	letrd	G -> suc a <= c
5	4	conv lt	G -> 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)