Theorem alleq2d ≪ | index | src | ≫

theorem alleq2d (_G: wff) (A: set) (_l1 _l2: nat):
  $ _G -> _l1 = _l2 $ >
  $ _G -> (all A _l1 <-> all A _l2) $;

Step	Hyp	Ref	Expression
1		eqsidd	_G -> A == A
2		hyp _h	_G -> _l1 = _l2
3	1, 2	alleqd	_G -> (all A _l1 <-> all A _l2)

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)