Theorem xpfst ≪ | index | src | ≫ 

theorem xpfst (A B: set) (a: nat): $ a e. Xp A B -> fst a e. A $;
StepHypRefExpression
1 elxp 
a e. Xp A B <-> fst a e. A /\ snd a e. B
2 anl 
fst a e. A /\ snd a e. B -> fst a e. A
3 1, 2 sylbi 
a e. Xp A B -> fst a e. A

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)