Theorem Listeqd | index | src |

theorem Listeqd (_G: wff) (_A1 _A2: set):
  $ _G -> _A1 == _A2 $ >
  $ _G -> List _A1 == List _A2 $;
StepHypRefExpression
1 hyp _Ah
_G -> _A1 == _A2
2 eqidd
_G -> n = n
3 1, 2 alleqd
_G -> (all _A1 n <-> all _A2 n)
4 3 abeqd
_G -> {n | all _A1 n} == {n | all _A2 n}
5 4 conv List
_G -> List _A1 == List _A2

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 (peano2, addeq, muleq)