Theorem greceq5d | index | src |

theorem greceq5d (_G: wff) (z: nat) (K F: set) (n _k1 _k2: nat):
  $ _G -> _k1 = _k2 $ >
  $ _G -> grec z K F n _k1 = grec z K F n _k2 $;
StepHypRefExpression
1 eqidd
_G -> z = z
2 eqsidd
_G -> K == K
3 eqsidd
_G -> F == F
4 eqidd
_G -> n = n
5 hyp _h
_G -> _k1 = _k2
6 1, 2, 3, 4, 5 greceqd
_G -> grec z K F n _k1 = grec z K F n _k2

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)