Theorem letr | index | src |

theorem letr (a b c: nat): $ a <= b -> b <= c -> a <= c $;
StepHypRefExpression
1 anl
a <= b /\ b <= c -> a <= b
2 anr
a <= b /\ b <= c -> b <= c
3 1, 2 letrd
a <= b /\ b <= c -> a <= c
4 3 exp
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)