Theorem funceq1d ≪ | index | src | ≫

theorem funceq1d (_G: wff) (_F1 _F2 A B: set):
  $ _G -> _F1 == _F2 $ >
  $ _G -> (func _F1 A B <-> func _F2 A B) $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> _F1 == _F2
2		eqsidd	_G -> A == A
3		eqsidd	_G -> B == B
4	1, 2, 3	funceqd	_G -> (func _F1 A B <-> func _F2 A B)

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)