Theorem receq1d ≪ | index | src | ≫

theorem receq1d (_G: wff) (_z1 _z2: nat) (S: set) (n: nat):
  $ _G -> _z1 = _z2 $ >
  $ _G -> rec _z1 S n = rec _z2 S n $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> _z1 = _z2
2		eqsidd	_G -> S == S
3		eqidd	_G -> n = n
4	1, 2, 3	receqd	_G -> rec _z1 S n = rec _z2 S n

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)