Theorem lreceq3d | index | src |

theorem lreceq3d (_G: wff) (z: nat) (S: set) (_n1 _n2: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> lrec z S _n1 = lrec z S _n2 $;
StepHypRefExpression
1 eqidd
_G -> z = z
2 eqsidd
_G -> S == S
3 hyp _h
_G -> _n1 = _n2
4 1, 2, 3 lreceqd
_G -> lrec z S _n1 = lrec 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)