Theorem rlreceq2d | index | src |

theorem rlreceq2d (_G: wff) (z: nat) (_S1 _S2: set) (n: nat):
  $ _G -> _S1 == _S2 $ >
  $ _G -> rlrec z _S1 n = rlrec z _S2 n $;
StepHypRefExpression
1 eqidd
_G -> z = z
2 hyp _h
_G -> _S1 == _S2
3 eqidd
_G -> n = n
4 1, 2, 3 rlreceqd
_G -> rlrec z _S1 n = rlrec 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)