Theorem xppi222 | index | src |

theorem xppi222 (A B C D: set) (a: nat):
  $ a e. Xp A (Xp B (Xp C D)) -> pi222 a e. D $;
StepHypRefExpression
1 xppi22
a e. Xp A (Xp B (Xp C D)) -> pi22 a e. Xp C D
2 xpsnd
pi22 a e. Xp C D -> snd (pi22 a) e. D
3 2 conv pi222
pi22 a e. Xp C D -> pi222 a e. D
4 1, 3 rsyl
a e. Xp A (Xp B (Xp C D)) -> pi222 a e. D

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)