Theorem xabfini ≪ | index | src | ≫

theorem xabfini (A: set) {x: nat} (B: set x):
  $ finite A $ >
  $ x e. A -> finite B $ >
  $ finite (X\ x e. A, B) $;

Step	Hyp	Ref	Expression
1		hyp h	finite A
2	1	a1i	T. -> finite A
3		hyp h2	x e. A -> finite B
4	3	anwr	T. /\ x e. A -> finite B
5	2, 4	xabfin	T. -> finite (X\ x e. A, B)
6	5	trud	finite (X\ x e. 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)