Theorem srecpeq1d ≪ | index | src | ≫

theorem srecpeq1d (_G: wff) (_A1 _A2: set) (n: nat):
  $ _G -> _A1 == _A2 $ >
  $ _G -> (srecp _A1 n <-> srecp _A2 n) $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> _A1 == _A2
2		eqidd	_G -> n = n
3	1, 2	srecpeqd	_G -> (srecp _A1 n <-> srecp _A2 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)