Theorem recneq3 ≪ | index | src | ≫

theorem recneq3 (z: nat) (S: set) (_n1 _n2: nat):
  $ _n1 = _n2 -> recn z S _n1 = recn z S _n2 $;

Step	Hyp	Ref	Expression
1		id	_n1 = _n2 -> _n1 = _n2
2	1	recneq3d	_n1 = _n2 -> recn z S _n1 = recn z S _n2

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)