Theorem leaddid1 | index | src |

theorem leaddid1 (a b: nat): $ a <= a + b $;
StepHypRefExpression
1 addeq2
x = b -> a + x = a + b
2 1 eqeq1d
x = b -> (a + x = a + b <-> a + b = a + b)
3 2 iexe
a + b = a + b -> E. x a + x = a + b
4 3 conv le
a + b = a + b -> a <= a + b
5 eqid
a + b = a + b
6 4, 5 ax_mp
a <= a + b

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_12), axs_peano (addeq)