Theorem funceq3d ≪ | index | src | ≫

theorem funceq3d (_G: wff) (F A _B1 _B2: set):
  $ _G -> _B1 == _B2 $ >
  $ _G -> (func F A _B1 <-> func F A _B2) $;

Step	Hyp	Ref	Expression
1		eqsidd	_G -> F == F
2		eqsidd	_G -> A == A
3		hyp _h	_G -> _B1 == _B2
4	1, 2, 3	funceqd	_G -> (func F A _B1 <-> func F A _B2)

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)