Theorem axext | index | src |

pub theorem axext (a b: nat): $ a == b -> a = b $;
StepHypRefExpression
1 ssle
a C_ b -> a <= b
2 eqss
a == b -> a C_ b
3 1, 2 syl
a == b -> a <= b
4 ssle
b C_ a -> b <= a
5 eqssr
a == b -> b C_ a
6 4, 5 syl
a == b -> b <= a
7 3, 6 leasymd
a == b -> a = b

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)