Theorem zsnd0 | index | src |

theorem zsnd0: $ zsnd 0 = 0 $;
StepHypRefExpression
1 eqtr3
zsnd (b0 0) = zsnd 0 -> zsnd (b0 0) = 0 -> zsnd 0 = 0
2 zsndeq
b0 0 = 0 -> zsnd (b0 0) = zsnd 0
3 b00
b0 0 = 0
4 2, 3 ax_mp
zsnd (b0 0) = zsnd 0
5 1, 4 ax_mp
zsnd (b0 0) = 0 -> zsnd 0 = 0
6 zsndb0
zsnd (b0 0) = 0
7 5, 6 ax_mp
zsnd 0 = 0

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)