Theorem alleq1 ≪ | index | src | ≫

theorem alleq1 (_A1 _A2: set) (l: nat):
  $ _A1 == _A2 -> (all _A1 l <-> all _A2 l) $;

Step	Hyp	Ref	Expression
1		id	_A1 == _A2 -> _A1 == _A2
2	1	alleq1d	_A1 == _A2 -> (all _A1 l <-> all _A2 l)

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)