Theorem lfneqd | index | src |

theorem lfneqd (_G: wff) (_F1 _F2: set) (_n1 _n2: nat):
  $ _G -> _F1 == _F2 $ >
  $ _G -> _n1 = _n2 $ >
  $ _G -> lfn _F1 _n1 = lfn _F2 _n2 $;
StepHypRefExpression
1 hyp _Fh
_G -> _F1 == _F2
2 eqidd
_G -> 0 = 0
3 hyp _nh
_G -> _n1 = _n2
4 1, 2, 3 lfnauxeqd
_G -> lfnaux _F1 0 _n1 = lfnaux _F2 0 _n2
5 4 conv lfn
_G -> lfn _F1 _n1 = lfn _F2 _n2

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)