Theorem receq2d ≪ | index | src | ≫

theorem receq2d (_G: wff) (z: nat) (_S1 _S2: set) (n: nat):
  $ _G -> _S1 == _S2 $ >
  $ _G -> rec z _S1 n = rec z _S2 n $;

Step	Hyp	Ref	Expression
1		eqidd	_G -> z = z
2		hyp _h	_G -> _S1 == _S2
3		eqidd	_G -> n = n
4	1, 2, 3	receqd	_G -> rec z _S1 n = rec z _S2 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)