Theorem xppi22 | index | src |

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

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)