Theorem elListHd ≪ | index | src | ≫

theorem elListHd (A: set) (G: wff) (a b: nat):
  $ G -> a : b e. List A $ >
  $ G -> a e. A $;

Step	Hyp	Ref	Expression
1		elListS	a : b e. List A <-> a e. A /\ b e. List A
2		hyp h	G -> a : b e. List A
3	1, 2	sylib	G -> a e. A /\ b e. List A
4	3	anld	G -> 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)