Theorem zsndneg | index | src |

theorem zsndneg (n: nat): $ zsnd (-uZ n) = zfst n $;
StepHypRefExpression
1 eqtr3
zfst (-uZ -uZ n) = zsnd (-uZ n) -> zfst (-uZ -uZ n) = zfst n -> zsnd (-uZ n) = zfst n
2 zfstneg
zfst (-uZ -uZ n) = zsnd (-uZ n)
3 1, 2 ax_mp
zfst (-uZ -uZ n) = zfst n -> zsnd (-uZ n) = zfst n
4 zfsteq
-uZ -uZ n = n -> zfst (-uZ -uZ n) = zfst n
5 znegneg
-uZ -uZ n = n
6 4, 5 ax_mp
zfst (-uZ -uZ n) = zfst n
7 3, 6 ax_mp
zsnd (-uZ n) = zfst n

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)