Theorem greceq2d | index | src |

theorem greceq2d (_G: wff) (z: nat) (_K1 _K2 F: set) (n k: nat):
  $ _G -> _K1 == _K2 $ >
  $ _G -> grec z _K1 F n k = grec z _K2 F n k $;
StepHypRefExpression
1 eqidd
_G -> z = z
2 hyp _h
_G -> _K1 == _K2
3 eqsidd
_G -> F == F
4 eqidd
_G -> n = n
5 eqidd
_G -> k = k
6 1, 2, 3, 4, 5 greceqd
_G -> grec z _K1 F n k = grec z _K2 F 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)