Theorem elListTl | index | src |

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