Theorem snoceq1d ≪ | index | src | ≫

theorem snoceq1d (_G: wff) (_l1 _l2 a: nat):
  $ _G -> _l1 = _l2 $ >
  $ _G -> _l1 |> a = _l2 |> a $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> _l1 = _l2
2		eqidd	_G -> a = a
3	1, 2	snoceqd	_G -> _l1 \|> a = _l2 \|> 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 (peano2, addeq, muleq)