Theorem prelxp ≪ | index | src | ≫ 

theorem prelxp (A B: set) (a b: nat): $ a, b e. Xp A B <-> a e. A /\ b e. B $;
StepHypRefExpression
1 eqsidd 
x = a -> B == B
2 1 elxab 
a, b e. X\ x e. A, B <-> a e. A /\ b e. B
3 2 conv Xp 
a, b e. Xp A B <-> a e. A /\ b e. B

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)