Theorem lfneq ≪ | index | src | ≫

theorem lfneq (_F1 _F2: set) (_n1 _n2: nat):
  $ _F1 == _F2 -> _n1 = _n2 -> lfn _F1 _n1 = lfn _F2 _n2 $;

Step	Hyp	Ref	Expression
1		anl	_F1 == _F2 /\ _n1 = _n2 -> _F1 == _F2
2		anr	_F1 == _F2 /\ _n1 = _n2 -> _n1 = _n2
3	1, 2	lfneqd	_F1 == _F2 /\ _n1 = _n2 -> lfn _F1 _n1 = lfn _F2 _n2
4	3	exp	_F1 == _F2 -> _n1 = _n2 -> 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)