Theorem xp02 | index | src |

theorem xp02 (A: set): $ Xp A 0 == 0 $;
StepHypRefExpression
1 eq0al
Xp A 0 == 0 <-> A. x ~x e. Xp A 0
2 xpsnd
x e. Xp A 0 -> snd x e. 0
3 el02
~snd x e. 0
4 2, 3 mt
~x e. Xp A 0
5 4 ax_gen
A. x ~x e. Xp A 0
6 1, 5 mpbir
Xp A 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)