Theorem grecaux2eq5d | index | src |

theorem grecaux2eq5d (_G: wff) (z: nat) (K F: set) (x _n1 _n2 k: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> grecaux2 z K F x _n1 k = grecaux2 z K F x _n2 k $;
StepHypRefExpression
1 eqidd
_G -> z = z
2 eqsidd
_G -> K == K
3 eqsidd
_G -> F == F
4 eqidd
_G -> x = x
5 hyp _h
_G -> _n1 = _n2
6 eqidd
_G -> k = k
7 1, 2, 3, 4, 5, 6 grecaux2eqd
_G -> grecaux2 z K F x _n1 k = grecaux2 z K F x _n2 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)