Theorem grecaux2eq6d | index | src |

theorem grecaux2eq6d (_G: wff) (z: nat) (K F: set) (x n _k1 _k2: nat):
  $ _G -> _k1 = _k2 $ >
  $ _G -> grecaux2 z K F x n _k1 = grecaux2 z K F x n _k2 $;
StepHypRefExpression
1 eqidd
_G -> z = z
2 eqsidd
_G -> K == K
3 eqsidd
_G -> F == F
4 eqidd
_G -> x = x
5 eqidd
_G -> n = n
6 hyp _h
_G -> _k1 = _k2
7 1, 2, 3, 4, 5, 6 grecaux2eqd
_G -> grecaux2 z K F x n _k1 = grecaux2 z K F x 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)