Theorem Listeqd ≪ | index | src | ≫

theorem Listeqd (_G: wff) (_A1 _A2: set):
  $ _G -> _A1 == _A2 $ >
  $ _G -> List _A1 == List _A2 $;

Step	Hyp	Ref	Expression
1		hyp _Ah	_G -> _A1 == _A2
2	1	alleq1d	_G -> (all _A1 n <-> all _A2 n)
3	2	abeqd	_G -> {n \| all _A1 n} == {n \| all _A2 n}
4	3	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)