Theorem greceq3d | index | src |

theorem greceq3d (_G: wff) (z: nat) (K _F1 _F2: set) (n k: nat):
  $ _G -> _F1 == _F2 $ >
  $ _G -> grec z K _F1 n k = grec z K _F2 n k $;
StepHypRefExpression
1 eqidd
_G -> z = z
2 eqsidd
_G -> K == K
3 hyp _h
_G -> _F1 == _F2
4 eqidd
_G -> n = n
5 eqidd
_G -> k = k
6 1, 2, 3, 4, 5 greceqd
_G -> grec z K _F1 n k = grec z K _F2 n k

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)