Theorem xpTd ≪ | index | src | ≫

theorem xpTd (A B: set) (G: wff) (a b: nat):
  $ G -> a e. A $ >
  $ G -> b e. B $ >
  $ G -> a, b e. Xp A B $;

Step	Hyp	Ref	Expression
1		prelxp	a, b e. Xp A B <-> a e. A /\ b e. B
2		hyp h1	G -> a e. A
3		hyp h2	G -> b e. B
4	2, 3	iand	G -> a e. A /\ b e. B
5	1, 4	sylibr	G -> a, b e. Xp A 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)